wehub-resource-sync
6185 lines
693 KiB
Plaintext
6185 lines
693 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "a0d75eb6",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.006951,
|
|
"end_time": "2026-06-13T03:11:49.804573+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:49.797622+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"# Chapter 5: Classical Simulation Methods\n",
|
|
"\n",
|
|
"**Docker image**: `ml4t`\n",
|
|
"\n",
|
|
"**Purpose**: Implement and compare classical Monte Carlo methods for generating\n",
|
|
"synthetic financial data, building the foundation for the learned generative\n",
|
|
"models that follow.\n",
|
|
"\n",
|
|
"This notebook teaches the **mechanics** of established Monte Carlo methods for\n",
|
|
"generating synthetic financial data. We cover both the underlying mathematics\n",
|
|
"and practical implementation, then show library shortcuts for production use.\n",
|
|
"\n",
|
|
"## Why Simulate?\n",
|
|
"\n",
|
|
"Historical market data provides only **one path** through an infinite space of\n",
|
|
"possibilities. Simulation generates alternative scenarios for:\n",
|
|
"\n",
|
|
"1. **Risk Management**: VaR, stress testing, tail risk assessment\n",
|
|
"2. **Backtesting**: Validate strategies beyond historical experience\n",
|
|
"3. **Data Augmentation**: Larger datasets for ML model training\n",
|
|
"4. **Privacy**: Share synthetic data without exposing proprietary signals\n",
|
|
"\n",
|
|
"## Learning Objectives\n",
|
|
"\n",
|
|
"After completing this notebook, you will be able to:\n",
|
|
"\n",
|
|
"1. **Implement** each classical stochastic model from scratch\n",
|
|
"2. **Explain** the assumptions and limitations of each model\n",
|
|
"3. **Choose** the appropriate model for your use case\n",
|
|
"4. **Use** library implementations for production work\n",
|
|
"\n",
|
|
"**Book Reference**: Chapter 5, Section 5.2 (Classical Simulation Baselines)\n",
|
|
"\n",
|
|
"**Prerequisites**: Basic probability and stochastic processes; familiarity\n",
|
|
"with NumPy array operations. Requires ETF data from Chapter 2 (`load_etfs()`).\n",
|
|
"\n",
|
|
"## Notebook Structure\n",
|
|
"\n",
|
|
"1. **Part 1**: Continuous-Time Price Models (GBM, Jump-Diffusion, OU, Heston)\n",
|
|
"2. **Part 2**: Discrete-Time Volatility Model (GARCH with calibration)\n",
|
|
"3. **Part 3**: Bootstrap Methods (IID, Block, Stationary)\n",
|
|
"4. **Part 4**: Model Comparison\n",
|
|
"\n",
|
|
"## Statistical Note\n",
|
|
"\n",
|
|
"We use **log-returns** throughout for consistency with continuous-time SDEs:\n",
|
|
"- Log-return: $r_t = \\ln(S_t / S_{t-1})$\n",
|
|
"- Kurtosis values are **Fisher (excess) kurtosis**: Gaussian = 0\n",
|
|
"\n",
|
|
"## References\n",
|
|
"\n",
|
|
"- Glasserman, P. (2003). \"Monte Carlo Methods in Financial Engineering\"\n",
|
|
"- Politis, D. & Romano, J. (1994). \"The Stationary Bootstrap\"\n",
|
|
"- Cont, R. (2001). \"Empirical Properties of Asset Returns: Stylized Facts\"\n",
|
|
"- Heston, S. (1993). \"A Closed-Form Solution for Options with Stochastic Volatility\""
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"id": "cb4e12b8",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:49.817943Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:49.817704Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:52.826939Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:52.826445Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 3.017301,
|
|
"end_time": "2026-06-13T03:11:52.827972+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:49.810671+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
".venv/lib/python3.14/site-packages/kaleido/scopes/plotly.py:32: DeprecationWarning: \n",
|
|
"Use of plotly.io.kaleido.scope.default_format is deprecated and support will be removed after September 2025.\n",
|
|
"Please use plotly.io.defaults.default_format instead.\n",
|
|
"\n",
|
|
" self.default_format = \"png\"\n",
|
|
".venv/lib/python3.14/site-packages/kaleido/scopes/plotly.py:33: DeprecationWarning: \n",
|
|
"Use of plotly.io.kaleido.scope.default_width is deprecated and support will be removed after September 2025.\n",
|
|
"Please use plotly.io.defaults.default_width instead.\n",
|
|
"\n",
|
|
" self.default_width = 700\n",
|
|
".venv/lib/python3.14/site-packages/kaleido/scopes/plotly.py:34: DeprecationWarning: \n",
|
|
"Use of plotly.io.kaleido.scope.default_height is deprecated and support will be removed after September 2025.\n",
|
|
"Please use plotly.io.defaults.default_height instead.\n",
|
|
"\n",
|
|
" self.default_height = 500\n",
|
|
".venv/lib/python3.14/site-packages/kaleido/scopes/plotly.py:35: DeprecationWarning: \n",
|
|
"Use of plotly.io.kaleido.scope.default_scale is deprecated and support will be removed after September 2025.\n",
|
|
"Please use plotly.io.defaults.default_scale instead.\n",
|
|
"\n",
|
|
" self.default_scale = 1\n",
|
|
".venv/lib/python3.14/site-packages/plotly/io/_kaleido.py:133: DeprecationWarning: \n",
|
|
"Use of plotly.io.kaleido.scope.mathjax is deprecated and support will be removed after September 2025.\n",
|
|
"Please use plotly.io.defaults.mathjax instead.\n",
|
|
"\n",
|
|
" setattr(self._scope, name, value)\n",
|
|
".venv/lib/python3.14/site-packages/plotly/io/_kaleido.py:141: DeprecationWarning: \n",
|
|
"Use of plotly.io.kaleido.scope.plotlyjs is deprecated and support will be removed after September 2025.\n",
|
|
"Please use plotly.io.defaults.plotlyjs instead.\n",
|
|
"\n",
|
|
" scope.plotlyjs = os.path.join(package_dir, \"plotly.min.js\")\n",
|
|
".venv/lib/python3.14/site-packages/plotly/io/_kaleido.py:147: DeprecationWarning: \n",
|
|
"Use of plotly.io.kaleido.scope.mathjax is deprecated and support will be removed after September 2025.\n",
|
|
"Please use plotly.io.defaults.mathjax instead.\n",
|
|
"\n",
|
|
" scope.mathjax = (\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"\"\"\"Classical Simulation Methods - Educational implementation of stochastic models.\"\"\"\n",
|
|
"\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"import numpy as np\n",
|
|
"import plotly.graph_objects as go\n",
|
|
"import polars as pl\n",
|
|
"import seaborn as sns\n",
|
|
"from arch import arch_model\n",
|
|
"from arch.bootstrap import IIDBootstrap, MovingBlockBootstrap, StationaryBootstrap\n",
|
|
"from ml4t.data.providers import SyntheticProvider\n",
|
|
"from plotly.subplots import make_subplots\n",
|
|
"from scipy.stats import kurtosis, skew\n",
|
|
"from statsmodels.tsa.stattools import acf\n",
|
|
"\n",
|
|
"from data import load_etfs\n",
|
|
"from utils.reproducibility import set_global_seeds\n",
|
|
"from utils.style import COLORS"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "822a6284",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:52.840290Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:52.840129Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:52.842144Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:52.841785Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.008681,
|
|
"end_time": "2026-06-13T03:11:52.842637+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.833956+00:00",
|
|
"status": "completed"
|
|
},
|
|
"tags": [
|
|
"parameters"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Production defaults (Papermill overrides for testing)\n",
|
|
"SEED = 42"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "db6862ec",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:52.853303Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:52.853195Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:52.894528Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:52.893921Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.047159,
|
|
"end_time": "2026-06-13T03:11:52.895318+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.848159+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"set_global_seeds(SEED)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2fa6b45c",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.003863,
|
|
"end_time": "2026-06-13T03:11:52.904552+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.900689+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"---\n",
|
|
"# Part 1: Continuous-Time Price Models\n",
|
|
"\n",
|
|
"These models specify stochastic differential equations (SDEs) for price dynamics.\n",
|
|
"Each captures different market phenomena:\n",
|
|
"\n",
|
|
"| Model | Key Feature | Best For |\n",
|
|
"|-------|-------------|----------|\n",
|
|
"| **GBM** | Log-normal prices, constant vol | Option pricing, baseline |\n",
|
|
"| **Jump-Diffusion** | Rare extreme moves | Crash scenarios, tail risk |\n",
|
|
"| **Mean-Reversion** | Prices drift to equilibrium | Spreads, commodities, rates |\n",
|
|
"| **Heston** | Stochastic volatility | Vol surfaces, leverage effect |\n",
|
|
"\n",
|
|
"We implement each from scratch using local RNG for reproducibility,\n",
|
|
"then show the equivalent library call."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "996ad1e3",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.003322,
|
|
"end_time": "2026-06-13T03:11:52.911523+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.908201+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## 1.1 Geometric Brownian Motion (GBM)\n",
|
|
"\n",
|
|
"The foundation of quantitative finance. Price $S$ follows the stochastic\n",
|
|
"differential equation:\n",
|
|
"\n",
|
|
"$$dS = \\mu S \\, dt + \\sigma S \\, dW$$\n",
|
|
"\n",
|
|
"where:\n",
|
|
"- $\\mu$ = drift (expected annual return)\n",
|
|
"- $\\sigma$ = volatility (annualized)\n",
|
|
"- $dW$ = Wiener process increment (Brownian motion)\n",
|
|
"\n",
|
|
"### Key Properties\n",
|
|
"\n",
|
|
"- **Log-returns are Gaussian**: $\\ln(S_{t+1}/S_t) \\sim N((\\mu - \\sigma^2/2)\\Delta t, \\sigma^2 \\Delta t)$\n",
|
|
"- **Prices are log-normal**: Always positive, no crashes below zero\n",
|
|
"- **No memory**: Future returns independent of past (no autocorrelation)\n",
|
|
"- **Constant volatility**: Same vol every day (unrealistic)\n",
|
|
"\n",
|
|
"### Discretization (Euler-Maruyama)\n",
|
|
"\n",
|
|
"$$S_{t+\\Delta t} = S_t \\exp\\left((\\mu - \\frac{\\sigma^2}{2}) \\Delta t + \\sigma \\sqrt{\\Delta t} \\, Z\\right)$$\n",
|
|
"\n",
|
|
"where $Z \\sim N(0,1)$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "618192db",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:52.920537Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:52.920414Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:52.923426Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:52.922865Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.008156,
|
|
"end_time": "2026-06-13T03:11:52.923891+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.915735+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def simulate_gbm(\n",
|
|
" n_steps: int,\n",
|
|
" mu: float,\n",
|
|
" sigma: float,\n",
|
|
" S0: float = 100.0,\n",
|
|
" dt: float = 1 / 252,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" Generate Geometric Brownian Motion price path.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" n_steps : int\n",
|
|
" Number of time steps\n",
|
|
" mu : float\n",
|
|
" Annual drift (expected return)\n",
|
|
" sigma : float\n",
|
|
" Annual volatility\n",
|
|
" S0 : float\n",
|
|
" Initial price\n",
|
|
" dt : float\n",
|
|
" Time step (1/252 for daily)\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator for reproducibility\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" np.ndarray\n",
|
|
" Price path of length n_steps + 1\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" # Standard normal random draws\n",
|
|
" Z = rng.standard_normal(n_steps)\n",
|
|
"\n",
|
|
" # Log-return for each step\n",
|
|
" log_returns = (mu - 0.5 * sigma**2) * dt + sigma * np.sqrt(dt) * Z\n",
|
|
"\n",
|
|
" # Cumulative sum gives log-prices, then exponentiate\n",
|
|
" log_prices = np.cumsum(log_returns)\n",
|
|
" prices = S0 * np.exp(log_prices)\n",
|
|
"\n",
|
|
" # Prepend initial price\n",
|
|
" return np.insert(prices, 0, S0)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "a49d3147",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.003301,
|
|
"end_time": "2026-06-13T03:11:52.930386+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.927085+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### GBM Simulation\n",
|
|
"\n",
|
|
"Generate 2 years of daily data and inspect the return distribution."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "91d5839d",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:52.937494Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:52.937286Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:52.942754Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:52.942111Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.009697,
|
|
"end_time": "2026-06-13T03:11:52.943171+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.933474+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"GBM simulation: 505 prices\n",
|
|
"Annualized return: 1.89%\n",
|
|
"Annualized volatility: 19.22%\n",
|
|
"Skewness: 0.0909 (Gaussian: 0)\n",
|
|
"Excess kurtosis: -0.0640 (Gaussian: 0)\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Example: 2 years of daily data\n",
|
|
"gbm_rng = np.random.default_rng(42)\n",
|
|
"gbm_prices = simulate_gbm(n_steps=504, mu=0.08, sigma=0.20, rng=gbm_rng)\n",
|
|
"gbm_returns = np.diff(np.log(gbm_prices))\n",
|
|
"\n",
|
|
"print(f\"GBM simulation: {len(gbm_prices)} prices\")\n",
|
|
"print(f\"Annualized return: {gbm_returns.mean() * 252:.2%}\")\n",
|
|
"print(f\"Annualized volatility: {gbm_returns.std() * np.sqrt(252):.2%}\")\n",
|
|
"print(f\"Skewness: {skew(gbm_returns):.4f} (Gaussian: 0)\")\n",
|
|
"print(f\"Excess kurtosis: {kurtosis(gbm_returns, fisher=True, bias=False):.4f} (Gaussian: 0)\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "8cc8b520",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.003961,
|
|
"end_time": "2026-06-13T03:11:52.951639+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.947678+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: GBM\n",
|
|
"\n",
|
|
"The `ml4t-data` package provides production implementations via `SyntheticProvider`:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"id": "cdd972cc",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:52.960353Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:52.960201Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.014035Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.013393Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.05868,
|
|
"end_time": "2026-06-13T03:11:53.014543+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:52.955863+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:52\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mRate limiter initialized \u001b[0m \u001b[36mmax_calls\u001b[0m=\u001b[35m1000\u001b[0m \u001b[36mperiod\u001b[0m=\u001b[35m1.0\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session initialized \u001b[0m \u001b[36mmax_connections\u001b[0m=\u001b[35m10\u001b[0m \u001b[36mtimeout\u001b[0m=\u001b[35m30.0\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mFetching OHLCV data \u001b[0m \u001b[36mend\u001b[0m=\u001b[35m2023-12-31\u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mstart\u001b[0m=\u001b[35m2022-01-01\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mGenerating 520 synthetic bars \u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mmodel\u001b[0m=\u001b[35mgbm\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mSuccessfully fetched OHLCV data\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mrows\u001b[0m=\u001b[35m520\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"SyntheticProvider GBM: 520 bars, final close=166.11\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"provider = SyntheticProvider(model=\"gbm\", annual_return=0.08, annual_volatility=0.20, seed=42)\n",
|
|
"df = provider.fetch_ohlcv(\"SYNTH\", \"2022-01-01\", \"2023-12-31\", \"daily\")\n",
|
|
"print(f\"SyntheticProvider GBM: {len(df)} bars, final close={float(df['close'][-1]):.2f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "6e1c6280",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.004082,
|
|
"end_time": "2026-06-13T03:11:53.023563+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.019481+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### GBM Limitations\n",
|
|
"\n",
|
|
"GBM assumes returns are **i.i.d. Gaussian**, which contradicts observed\n",
|
|
"\"stylized facts\" of financial returns:\n",
|
|
"\n",
|
|
"1. **Fat tails**: Real returns have excess kurtosis (more extremes than Gaussian)\n",
|
|
"2. **Volatility clustering**: High-vol days tend to follow high-vol days\n",
|
|
"3. **Leverage effect**: Negative returns often increase future volatility\n",
|
|
"\n",
|
|
"Despite these limitations, GBM remains the workhorse for option pricing\n",
|
|
"(Black-Scholes) due to its analytical tractability."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "20978bf2",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.003534,
|
|
"end_time": "2026-06-13T03:11:53.030723+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.027189+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## 1.2 Jump-Diffusion (Merton Model)\n",
|
|
"\n",
|
|
"Adds occasional extreme moves to GBM via a compound Poisson process:\n",
|
|
"\n",
|
|
"$$dS = \\mu S \\, dt + \\sigma S \\, dW + S(e^Y - 1) \\, dN$$\n",
|
|
"\n",
|
|
"where:\n",
|
|
"- $dN$ = Poisson process with intensity $\\lambda$ (jumps per year)\n",
|
|
"- $Y \\sim N(\\mu_J, \\sigma_J^2)$ = log jump size\n",
|
|
"\n",
|
|
"### Drift Compensator\n",
|
|
"\n",
|
|
"To ensure $\\mu$ represents the *total* expected return (including jumps),\n",
|
|
"we subtract the expected jump contribution:\n",
|
|
"\n",
|
|
"$$k = \\mathbb{E}[e^Y - 1] = \\exp(\\mu_J + \\tfrac{1}{2}\\sigma_J^2) - 1$$\n",
|
|
"\n",
|
|
"### Discretization\n",
|
|
"\n",
|
|
"$$S_{t+\\Delta t} = S_t \\exp\\left((\\mu - \\lambda k - \\frac{\\sigma^2}{2}) \\Delta t\n",
|
|
" + \\sigma \\sqrt{\\Delta t} Z + \\sum_{i=1}^{N_t} Y_i\\right)$$\n",
|
|
"\n",
|
|
"where $N_t \\sim \\text{Poisson}(\\lambda \\Delta t)$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "0fbdb7dd",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.039538Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.039250Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.044266Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.043693Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.010323,
|
|
"end_time": "2026-06-13T03:11:53.044710+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.034387+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def simulate_jump_diffusion(\n",
|
|
" n_steps: int,\n",
|
|
" mu: float,\n",
|
|
" sigma: float,\n",
|
|
" lambda_: float,\n",
|
|
" mu_jump: float,\n",
|
|
" sigma_jump: float,\n",
|
|
" S0: float = 100.0,\n",
|
|
" dt: float = 1 / 252,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" Generate Merton jump-diffusion price path with compensated drift.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" n_steps : int\n",
|
|
" Number of time steps\n",
|
|
" mu : float\n",
|
|
" Total annual drift (including jump contribution)\n",
|
|
" sigma : float\n",
|
|
" Annual volatility (diffusion part)\n",
|
|
" lambda_ : float\n",
|
|
" Jump intensity (expected jumps per year)\n",
|
|
" mu_jump : float\n",
|
|
" Mean of log jump size Y ~ N(mu_jump, sigma_jump^2)\n",
|
|
" sigma_jump : float\n",
|
|
" Std of log jump size\n",
|
|
" S0 : float\n",
|
|
" Initial price\n",
|
|
" dt : float\n",
|
|
" Time step\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" np.ndarray\n",
|
|
" Price path of length n_steps + 1\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" # Jump compensator: E[e^Y - 1] so mu remains the total expected return\n",
|
|
" k = np.exp(mu_jump + 0.5 * sigma_jump**2) - 1\n",
|
|
"\n",
|
|
" # Diffusion component with compensated drift\n",
|
|
" Z = rng.standard_normal(n_steps)\n",
|
|
" drift_compensated = mu - lambda_ * k - 0.5 * sigma**2\n",
|
|
" diffusion = drift_compensated * dt + sigma * np.sqrt(dt) * Z\n",
|
|
"\n",
|
|
" # Jump component: compound Poisson\n",
|
|
" N_jumps = rng.poisson(lambda_ * dt, n_steps)\n",
|
|
" jump_component = np.zeros(n_steps)\n",
|
|
"\n",
|
|
" # Vectorized: for steps with jumps, sample and sum log jump sizes\n",
|
|
" steps_with_jumps = np.where(N_jumps > 0)[0]\n",
|
|
" for t in steps_with_jumps:\n",
|
|
" jump_sizes = rng.normal(mu_jump, sigma_jump, N_jumps[t])\n",
|
|
" jump_component[t] = np.sum(jump_sizes)\n",
|
|
"\n",
|
|
" # Combine and build price path\n",
|
|
" log_returns = diffusion + jump_component\n",
|
|
" log_prices = np.cumsum(log_returns)\n",
|
|
" prices = S0 * np.exp(log_prices)\n",
|
|
"\n",
|
|
" return np.insert(prices, 0, S0)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1c1bc830",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.00472,
|
|
"end_time": "2026-06-13T03:11:53.055123+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.050403+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Jump-Diffusion Simulation\n",
|
|
"\n",
|
|
"Simulate with negative jumps (crash scenarios). With `lambda_=5` we expect\n",
|
|
"roughly 5 jumps per year; `mu_jump=-0.03` means each jump averages 3% down."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "c72dd9a7",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.064595Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.064441Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.069796Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.069438Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.010782,
|
|
"end_time": "2026-06-13T03:11:53.070117+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.059335+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Jump-Diffusion simulation: 505 prices\n",
|
|
"Jump compensator k: -0.0288 (subtracted from drift)\n",
|
|
"Annualized return: 7.80%\n",
|
|
"Annualized volatility: 17.90%\n",
|
|
"Skewness: -1.5179\n",
|
|
"Excess kurtosis: 8.1871 (> 0 from jumps)\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Example: negative jumps (crash scenarios)\n",
|
|
"# lambda=5 means ~5 jumps/year; mu_jump=-0.03 means avg 3% down-jump\n",
|
|
"jd_rng = np.random.default_rng(43)\n",
|
|
"jd_prices = simulate_jump_diffusion(\n",
|
|
" n_steps=504,\n",
|
|
" mu=0.08, # Total expected return\n",
|
|
" sigma=0.15, # Diffusion volatility\n",
|
|
" lambda_=5.0,\n",
|
|
" mu_jump=-0.03, # Mean log jump (negative = down)\n",
|
|
" sigma_jump=0.04,\n",
|
|
" rng=jd_rng,\n",
|
|
")\n",
|
|
"jd_returns = np.diff(np.log(jd_prices))\n",
|
|
"\n",
|
|
"# Show jump compensator\n",
|
|
"k = np.exp(-0.03 + 0.5 * 0.04**2) - 1\n",
|
|
"print(f\"Jump-Diffusion simulation: {len(jd_prices)} prices\")\n",
|
|
"print(f\"Jump compensator k: {k:.4f} (subtracted from drift)\")\n",
|
|
"print(f\"Annualized return: {jd_returns.mean() * 252:.2%}\")\n",
|
|
"print(f\"Annualized volatility: {jd_returns.std() * np.sqrt(252):.2%}\")\n",
|
|
"print(f\"Skewness: {skew(jd_returns):.4f}\")\n",
|
|
"print(f\"Excess kurtosis: {kurtosis(jd_returns, fisher=True, bias=False):.4f} (> 0 from jumps)\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2f2b8098",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.002953,
|
|
"end_time": "2026-06-13T03:11:53.076577+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.073624+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: Jump-Diffusion"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "c83cfeca",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.083486Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.083290Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.104663Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.103975Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.025642,
|
|
"end_time": "2026-06-13T03:11:53.105249+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.079607+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mRate limiter initialized \u001b[0m \u001b[36mmax_calls\u001b[0m=\u001b[35m1000\u001b[0m \u001b[36mperiod\u001b[0m=\u001b[35m1.0\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session initialized \u001b[0m \u001b[36mmax_connections\u001b[0m=\u001b[35m10\u001b[0m \u001b[36mtimeout\u001b[0m=\u001b[35m30.0\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session closed \u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mFetching OHLCV data \u001b[0m \u001b[36mend\u001b[0m=\u001b[35m2023-12-31\u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mstart\u001b[0m=\u001b[35m2022-01-01\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mGenerating 520 synthetic bars \u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mmodel\u001b[0m=\u001b[35mgbm_jump\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mSuccessfully fetched OHLCV data\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mrows\u001b[0m=\u001b[35m520\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"SyntheticProvider Jump-Diffusion: 520 bars, final close=110.87\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"provider = SyntheticProvider(model=\"gbm_jump\", annual_return=0.08, annual_volatility=0.15, seed=43)\n",
|
|
"df = provider.fetch_ohlcv(\"SYNTH\", \"2022-01-01\", \"2023-12-31\", \"daily\")\n",
|
|
"print(f\"SyntheticProvider Jump-Diffusion: {len(df)} bars, final close={float(df['close'][-1]):.2f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "71b65ec5",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.00427,
|
|
"end_time": "2026-06-13T03:11:53.113921+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.109651+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## 1.3 Mean-Reversion (Ornstein-Uhlenbeck)\n",
|
|
"\n",
|
|
"Prices gravitate toward a long-term equilibrium $\\theta$:\n",
|
|
"\n",
|
|
"$$d(\\log S) = \\kappa(\\theta - \\log S) \\, dt + \\sigma \\, dW$$\n",
|
|
"\n",
|
|
"where:\n",
|
|
"- $\\kappa$ = speed of mean reversion\n",
|
|
"- $\\theta$ = long-term mean (log-price level)\n",
|
|
"- Half-life: $t_{1/2} = \\ln(2) / \\kappa$\n",
|
|
"\n",
|
|
"### Key Properties\n",
|
|
"\n",
|
|
"- **Stationary**: Prices fluctuate around equilibrium\n",
|
|
"- **No trends**: Can't capture bull/bear markets\n",
|
|
"- **Negative autocorrelation**: Today's move partially reversed tomorrow\n",
|
|
"\n",
|
|
"### Discretization Options\n",
|
|
"\n",
|
|
"**Euler-Maruyama** (approximate):\n",
|
|
"$$X_{t+\\Delta t} = X_t + \\kappa(\\theta - X_t)\\Delta t + \\sigma\\sqrt{\\Delta t} Z$$\n",
|
|
"\n",
|
|
"**Exact transition** (closed-form for OU):\n",
|
|
"$$X_{t+\\Delta t} = \\theta + (X_t - \\theta)e^{-\\kappa\\Delta t}\n",
|
|
" + \\sigma\\sqrt{\\frac{1 - e^{-2\\kappa\\Delta t}}{2\\kappa}} Z$$\n",
|
|
"\n",
|
|
"We implement both to compare discretization error."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"id": "e58e3482",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.123090Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.122904Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.126911Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.126367Z"
|
|
},
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.009322,
|
|
"end_time": "2026-06-13T03:11:53.127506+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.118184+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def simulate_mean_reversion_euler(\n",
|
|
" n_steps: int,\n",
|
|
" kappa: float,\n",
|
|
" theta: float,\n",
|
|
" sigma: float,\n",
|
|
" S0: float = 100.0,\n",
|
|
" dt: float = 1 / 252,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" Generate OU process using Euler-Maruyama discretization.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" n_steps : int\n",
|
|
" Number of time steps\n",
|
|
" kappa : float\n",
|
|
" Mean reversion speed (annualized)\n",
|
|
" theta : float\n",
|
|
" Long-term mean (log-price level)\n",
|
|
" sigma : float\n",
|
|
" Volatility (annualized)\n",
|
|
" S0 : float\n",
|
|
" Initial price\n",
|
|
" dt : float\n",
|
|
" Time step\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" np.ndarray\n",
|
|
" Price path of length n_steps + 1\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" log_prices = np.zeros(n_steps + 1)\n",
|
|
" log_prices[0] = np.log(S0)\n",
|
|
"\n",
|
|
" Z = rng.standard_normal(n_steps)\n",
|
|
"\n",
|
|
" for t in range(n_steps):\n",
|
|
" log_prices[t + 1] = (\n",
|
|
" log_prices[t] + kappa * (theta - log_prices[t]) * dt + sigma * np.sqrt(dt) * Z[t]\n",
|
|
" )\n",
|
|
"\n",
|
|
" return np.exp(log_prices)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9ddef997",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.003844,
|
|
"end_time": "2026-06-13T03:11:53.137167+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.133323+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Exact Transition Density\n",
|
|
"\n",
|
|
"The OU process has a closed-form transition density, eliminating\n",
|
|
"discretization error entirely. We implement both to compare accuracy."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"id": "91e2ccf5",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.146188Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.146027Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.149633Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.149131Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.008805,
|
|
"end_time": "2026-06-13T03:11:53.150016+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.141211+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def simulate_mean_reversion_exact(\n",
|
|
" n_steps: int,\n",
|
|
" kappa: float,\n",
|
|
" theta: float,\n",
|
|
" sigma: float,\n",
|
|
" S0: float = 100.0,\n",
|
|
" dt: float = 1 / 252,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" Generate OU process using exact transition density.\n",
|
|
"\n",
|
|
" The exact solution eliminates discretization error entirely.\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" log_prices = np.zeros(n_steps + 1)\n",
|
|
" log_prices[0] = np.log(S0)\n",
|
|
"\n",
|
|
" # Precompute constants\n",
|
|
" exp_neg_kappa_dt = np.exp(-kappa * dt)\n",
|
|
" std_dev = sigma * np.sqrt((1 - np.exp(-2 * kappa * dt)) / (2 * kappa))\n",
|
|
"\n",
|
|
" Z = rng.standard_normal(n_steps)\n",
|
|
"\n",
|
|
" for t in range(n_steps):\n",
|
|
" log_prices[t + 1] = theta + (log_prices[t] - theta) * exp_neg_kappa_dt + std_dev * Z[t]\n",
|
|
"\n",
|
|
" return np.exp(log_prices)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "183cffa9",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.003147,
|
|
"end_time": "2026-06-13T03:11:53.156565+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.153418+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Mean-Reversion Simulation\n",
|
|
"\n",
|
|
"Compare exact vs Euler discretization. With `kappa=2`, the half-life is\n",
|
|
"$\\ln(2)/2 \\approx 0.35$ years (87 trading days)."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"id": "f291c661",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.163553Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.163254Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.169347Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.168734Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.010152,
|
|
"end_time": "2026-06-13T03:11:53.169705+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.159553+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Mean-Reversion (exact) simulation: 505 prices\n",
|
|
"Half-life: 87 trading days\n",
|
|
"Final price: 99.60 (equilibrium: 100)\n",
|
|
"Return autocorr(1): -0.0615\n",
|
|
"Euler vs Exact max difference: 0.047112\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Example: mean-reverting around 100 using exact discretization\n",
|
|
"# kappa=2 gives half-life of ln(2)/2 ≈ 0.35 years (87 trading days)\n",
|
|
"mr_rng = np.random.default_rng(44)\n",
|
|
"mr_prices = simulate_mean_reversion_exact(\n",
|
|
" n_steps=504,\n",
|
|
" kappa=2.0,\n",
|
|
" theta=np.log(100), # Long-term mean at 100\n",
|
|
" sigma=0.15,\n",
|
|
" rng=mr_rng,\n",
|
|
")\n",
|
|
"mr_returns = np.diff(np.log(mr_prices))\n",
|
|
"\n",
|
|
"half_life_days = np.log(2) / 2.0 * 252\n",
|
|
"print(f\"Mean-Reversion (exact) simulation: {len(mr_prices)} prices\")\n",
|
|
"print(f\"Half-life: {half_life_days:.0f} trading days\")\n",
|
|
"print(f\"Final price: {mr_prices[-1]:.2f} (equilibrium: 100)\")\n",
|
|
"print(f\"Return autocorr(1): {np.corrcoef(mr_returns[:-1], mr_returns[1:])[0, 1]:.4f}\")\n",
|
|
"\n",
|
|
"# Compare Euler vs Exact discretization\n",
|
|
"mr_rng_euler = np.random.default_rng(44) # Same seed\n",
|
|
"mr_euler = simulate_mean_reversion_euler(\n",
|
|
" n_steps=504, kappa=2.0, theta=np.log(100), sigma=0.15, rng=mr_rng_euler\n",
|
|
")\n",
|
|
"max_diff = np.max(np.abs(mr_prices - mr_euler))\n",
|
|
"print(f\"Euler vs Exact max difference: {max_diff:.6f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d7b94c83",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.003924,
|
|
"end_time": "2026-06-13T03:11:53.177129+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.173205+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: Mean-Reversion"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"id": "823402a9",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.186592Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.186455Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.202725Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.201923Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.021936,
|
|
"end_time": "2026-06-13T03:11:53.203178+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.181242+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mRate limiter initialized \u001b[0m \u001b[36mmax_calls\u001b[0m=\u001b[35m1000\u001b[0m \u001b[36mperiod\u001b[0m=\u001b[35m1.0\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session initialized \u001b[0m \u001b[36mmax_connections\u001b[0m=\u001b[35m10\u001b[0m \u001b[36mtimeout\u001b[0m=\u001b[35m30.0\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session closed \u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mFetching OHLCV data \u001b[0m \u001b[36mend\u001b[0m=\u001b[35m2023-12-31\u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mstart\u001b[0m=\u001b[35m2022-01-01\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mGenerating 520 synthetic bars \u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mmodel\u001b[0m=\u001b[35mmean_revert\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mSuccessfully fetched OHLCV data\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mrows\u001b[0m=\u001b[35m520\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"SyntheticProvider Mean-Revert: 520 bars, final close=107.12\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"provider = SyntheticProvider(model=\"mean_revert\", annual_volatility=0.15, seed=44)\n",
|
|
"df = provider.fetch_ohlcv(\"SYNTH\", \"2022-01-01\", \"2023-12-31\", \"daily\")\n",
|
|
"print(f\"SyntheticProvider Mean-Revert: {len(df)} bars, final close={float(df['close'][-1]):.2f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c5558ec5",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.004327,
|
|
"end_time": "2026-06-13T03:11:53.212783+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.208456+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## 1.4 Heston (Stochastic Volatility)\n",
|
|
"\n",
|
|
"Volatility itself is random, following a separate mean-reverting process:\n",
|
|
"\n",
|
|
"$$dS = \\mu S \\, dt + \\sqrt{v} S \\, dW_S$$\n",
|
|
"$$dv = \\kappa(\\theta - v) \\, dt + \\xi \\sqrt{v} \\, dW_v$$\n",
|
|
"$$\\text{Corr}(dW_S, dW_v) = \\rho$$\n",
|
|
"\n",
|
|
"where:\n",
|
|
"- $v$ = instantaneous variance\n",
|
|
"- $\\kappa$ = variance mean-reversion speed\n",
|
|
"- $\\theta$ = long-term variance\n",
|
|
"- $\\xi$ = volatility of volatility (\"vol of vol\")\n",
|
|
"- $\\rho$ = correlation between price and variance shocks (leverage effect)\n",
|
|
"\n",
|
|
"### Key Properties\n",
|
|
"\n",
|
|
"- **Stochastic volatility**: Vol changes unpredictably\n",
|
|
"- **Leverage effect**: $\\rho < 0$ means price drops increase volatility\n",
|
|
"- **Fat tails**: From randomness in volatility\n",
|
|
"- **Volatility clustering**: From mean-reversion in variance\n",
|
|
"- **Feller condition**: $2\\kappa\\theta > \\xi^2$ prevents variance from hitting zero\n",
|
|
"\n",
|
|
"### Discretization: Full Truncation Euler\n",
|
|
"\n",
|
|
"To handle potential negative variance, we use **full truncation**:\n",
|
|
"apply $\\max(v, 0)$ consistently in both drift and diffusion terms."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"id": "44ef9c8d",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.222412Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.222134Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.226374Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.226009Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.009531,
|
|
"end_time": "2026-06-13T03:11:53.226755+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.217224+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def simulate_heston(\n",
|
|
" n_steps: int,\n",
|
|
" mu: float,\n",
|
|
" v0: float,\n",
|
|
" kappa: float,\n",
|
|
" theta: float,\n",
|
|
" xi: float,\n",
|
|
" rho: float,\n",
|
|
" S0: float = 100.0,\n",
|
|
" dt: float = 1 / 252,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> tuple[np.ndarray, np.ndarray]:\n",
|
|
" \"\"\"\n",
|
|
" Generate Heston stochastic volatility path using full truncation Euler.\n",
|
|
"\n",
|
|
" Full truncation applies max(v, 0) to the current variance before\n",
|
|
" computing both drift and diffusion terms, ensuring consistency.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" n_steps : int\n",
|
|
" Number of time steps\n",
|
|
" mu : float\n",
|
|
" Drift\n",
|
|
" v0 : float\n",
|
|
" Initial variance\n",
|
|
" kappa : float\n",
|
|
" Variance mean-reversion speed\n",
|
|
" theta : float\n",
|
|
" Long-term variance\n",
|
|
" xi : float\n",
|
|
" Volatility of variance (vol of vol)\n",
|
|
" rho : float\n",
|
|
" Correlation between price and variance shocks\n",
|
|
" S0 : float\n",
|
|
" Initial price\n",
|
|
" dt : float\n",
|
|
" Time step\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" tuple[np.ndarray, np.ndarray]\n",
|
|
" Price path and variance path\n",
|
|
"\n",
|
|
" Note\n",
|
|
" ----\n",
|
|
" For production use, consider Andersen's QE scheme which has better\n",
|
|
" accuracy near the boundary.\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" prices = np.zeros(n_steps + 1)\n",
|
|
" variance = np.zeros(n_steps + 1)\n",
|
|
" prices[0] = S0\n",
|
|
" variance[0] = v0\n",
|
|
"\n",
|
|
" sqrt_dt = np.sqrt(dt)\n",
|
|
"\n",
|
|
" for t in range(n_steps):\n",
|
|
" # Full truncation: apply floor BEFORE computing terms\n",
|
|
" v_t = max(variance[t], 0)\n",
|
|
" sqrt_v_t = np.sqrt(v_t)\n",
|
|
"\n",
|
|
" # Correlated Brownian motions\n",
|
|
" Z1 = rng.standard_normal()\n",
|
|
" Z2 = rng.standard_normal()\n",
|
|
" W_v = Z1\n",
|
|
" W_S = rho * Z1 + np.sqrt(1 - rho**2) * Z2\n",
|
|
"\n",
|
|
" # Variance update (full truncation Euler)\n",
|
|
" variance[t + 1] = v_t + kappa * (theta - v_t) * dt + xi * sqrt_v_t * sqrt_dt * W_v\n",
|
|
" # Floor the result for next iteration\n",
|
|
" variance[t + 1] = max(variance[t + 1], 0)\n",
|
|
"\n",
|
|
" # Price update\n",
|
|
" prices[t + 1] = prices[t] * np.exp((mu - 0.5 * v_t) * dt + sqrt_v_t * sqrt_dt * W_S)\n",
|
|
"\n",
|
|
" return prices, variance"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2b012633",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.004467,
|
|
"end_time": "2026-06-13T03:11:53.235648+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.231181+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Heston Simulation\n",
|
|
"\n",
|
|
"Simulate with typical parameters. We verify the Feller condition\n",
|
|
"($2\\kappa\\theta > \\xi^2$) to ensure variance stays positive."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"id": "83bb568d",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.245728Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.245588Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.251248Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.250688Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.011713,
|
|
"end_time": "2026-06-13T03:11:53.251624+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.239911+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Heston simulation: 505 prices\n",
|
|
"Feller condition: 2*kappa*theta = 0.40 > xi^2 = 0.09: OK\n",
|
|
"Initial vol: 20.0%\n",
|
|
"Final vol: 15.7%\n",
|
|
"Min variance (should be >= 0): 0.006035\n",
|
|
"Excess kurtosis: 0.9388\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Example: typical Heston parameters\n",
|
|
"# Feller condition: 2*5*0.04 = 0.4 > 0.3^2 = 0.09 [OK]\n",
|
|
"heston_rng = np.random.default_rng(45)\n",
|
|
"heston_prices, heston_var = simulate_heston(\n",
|
|
" n_steps=504,\n",
|
|
" mu=0.05,\n",
|
|
" v0=0.04, # Initial vol = 20%\n",
|
|
" kappa=5.0, # Fast mean reversion\n",
|
|
" theta=0.04, # Long-term vol = 20%\n",
|
|
" xi=0.3, # Vol of vol = 30%\n",
|
|
" rho=-0.7, # Strong leverage effect\n",
|
|
" rng=heston_rng,\n",
|
|
")\n",
|
|
"heston_returns = np.diff(np.log(heston_prices))\n",
|
|
"\n",
|
|
"# Verify Feller condition\n",
|
|
"feller_lhs = 2 * 5.0 * 0.04\n",
|
|
"feller_rhs = 0.3**2\n",
|
|
"print(f\"Heston simulation: {len(heston_prices)} prices\")\n",
|
|
"print(\n",
|
|
" f\"Feller condition: 2*kappa*theta = {feller_lhs:.2f} > xi^2 = {feller_rhs:.2f}: \"\n",
|
|
" f\"{'OK' if feller_lhs > feller_rhs else 'VIOLATED'}\"\n",
|
|
")\n",
|
|
"print(f\"Initial vol: {np.sqrt(heston_var[0]) * 100:.1f}%\")\n",
|
|
"print(f\"Final vol: {np.sqrt(heston_var[-1]) * 100:.1f}%\")\n",
|
|
"print(f\"Min variance (should be >= 0): {heston_var.min():.6f}\")\n",
|
|
"print(f\"Excess kurtosis: {kurtosis(heston_returns, fisher=True, bias=False):.4f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1eb00cf8",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.00415,
|
|
"end_time": "2026-06-13T03:11:53.260318+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.256168+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: Heston"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"id": "ea5c5274",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.270325Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.270153Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.283201Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.282655Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.019081,
|
|
"end_time": "2026-06-13T03:11:53.283519+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.264438+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mRate limiter initialized \u001b[0m \u001b[36mmax_calls\u001b[0m=\u001b[35m1000\u001b[0m \u001b[36mperiod\u001b[0m=\u001b[35m1.0\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session initialized \u001b[0m \u001b[36mmax_connections\u001b[0m=\u001b[35m10\u001b[0m \u001b[36mtimeout\u001b[0m=\u001b[35m30.0\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session closed \u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mFetching OHLCV data \u001b[0m \u001b[36mend\u001b[0m=\u001b[35m2023-12-31\u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mstart\u001b[0m=\u001b[35m2022-01-01\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mGenerating 520 synthetic bars \u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mmodel\u001b[0m=\u001b[35mheston\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mSuccessfully fetched OHLCV data\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mrows\u001b[0m=\u001b[35m520\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"SyntheticProvider Heston: 520 bars, final close=129.38\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"provider = SyntheticProvider(model=\"heston\", annual_volatility=0.20, heston_xi=0.3, seed=45)\n",
|
|
"df = provider.fetch_ohlcv(\"SYNTH\", \"2022-01-01\", \"2023-12-31\", \"daily\")\n",
|
|
"print(f\"SyntheticProvider Heston: {len(df)} bars, final close={float(df['close'][-1]):.2f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b42c971a",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.004986,
|
|
"end_time": "2026-06-13T03:11:53.293293+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.288307+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"---\n",
|
|
"# Part 2: Discrete-Time Volatility Model (GARCH)\n",
|
|
"\n",
|
|
"Unlike the continuous-time SDEs above, GARCH is a **discrete-time model**\n",
|
|
"for conditional variance. It models how return volatility evolves based on\n",
|
|
"past shocks.\n",
|
|
"\n",
|
|
"## GARCH(1,1)\n",
|
|
"\n",
|
|
"$$r_t = \\mu + \\sigma_t \\varepsilon_t, \\quad \\varepsilon_t \\sim N(0,1)$$\n",
|
|
"$$\\sigma^2_t = \\omega + \\alpha (r_{t-1} - \\mu)^2 + \\beta \\sigma^2_{t-1}$$\n",
|
|
"\n",
|
|
"where:\n",
|
|
"- $\\mu$ = unconditional mean return (drift)\n",
|
|
"- $\\omega$ = base variance (intercept)\n",
|
|
"- $\\alpha$ = reaction to recent shocks (news impact)\n",
|
|
"- $\\beta$ = persistence of past variance (memory)\n",
|
|
"- $\\alpha + \\beta < 1$ required for stationarity\n",
|
|
"\n",
|
|
"### Key Properties\n",
|
|
"\n",
|
|
"- **Volatility clustering**: $\\beta > 0$ means vol persists\n",
|
|
"- **Fat tails**: From time-varying volatility\n",
|
|
"- **Mean-reverting volatility**: Unconditional variance = $\\omega / (1 - \\alpha - \\beta)$\n",
|
|
"- **Leverage effect**: Requires asymmetric extensions (GJR-GARCH, EGARCH)\n",
|
|
"\n",
|
|
"### GARCH vs Heston\n",
|
|
"\n",
|
|
"| Aspect | GARCH | Heston |\n",
|
|
"|--------|-------|--------|\n",
|
|
"| Time | Discrete | Continuous |\n",
|
|
"| Leverage | Extensions needed | Built-in ($\\rho$) |\n",
|
|
"| Calibration | MLE from data | Option surface |\n",
|
|
"| Analytical | Limited | Semi-closed form |\n",
|
|
"\n",
|
|
"## Calibration: Fitting GARCH to Data\n",
|
|
"\n",
|
|
"Unlike SDEs where we **choose** parameters (drift, volatility), GARCH is\n",
|
|
"typically **fitted** to historical data via maximum likelihood estimation."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"id": "d410f36c",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.305970Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.305683Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.335818Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.335120Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.03732,
|
|
"end_time": "2026-06-13T03:11:53.336374+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.299054+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"SPY log-returns: 5030 observations\n",
|
|
"Mean: 0.0408% daily\n",
|
|
"Std: 1.2220%\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Load SPY returns for GARCH calibration\n",
|
|
"etf_data = load_etfs()\n",
|
|
"spy_close = (\n",
|
|
" etf_data.filter(pl.col(\"symbol\") == \"SPY\")\n",
|
|
" .sort(\"timestamp\")\n",
|
|
" .select(\"close\")\n",
|
|
" .to_series()\n",
|
|
" .to_numpy()\n",
|
|
")\n",
|
|
"\n",
|
|
"# Compute log returns in percent (arch library convention; matches exp(cumsum) reconstruction)\n",
|
|
"spy_log_returns_pct = np.diff(np.log(spy_close)) * 100\n",
|
|
"\n",
|
|
"print(f\"SPY log-returns: {len(spy_log_returns_pct)} observations\")\n",
|
|
"print(f\"Mean: {spy_log_returns_pct.mean():.4f}% daily\")\n",
|
|
"print(f\"Std: {spy_log_returns_pct.std():.4f}%\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ba781a8c",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.006512,
|
|
"end_time": "2026-06-13T03:11:53.349456+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.342944+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Fit GARCH(1,1) to SPY"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"id": "d04e5fb1",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.365141Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.364949Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.427667Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.426372Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.072863,
|
|
"end_time": "2026-06-13T03:11:53.429514+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.356651+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Calibrated GARCH(1,1) parameters:\n",
|
|
" mu (mean): 0.081175% daily\n",
|
|
" omega: 0.030613\n",
|
|
" alpha (news): 0.1404\n",
|
|
" beta (memory): 0.8362\n",
|
|
" persistence: 0.9766\n",
|
|
" unconditional vol: 1.1450% daily\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Fit GARCH(1,1) model\n",
|
|
"am = arch_model(spy_log_returns_pct, mean=\"Constant\", vol=\"GARCH\", p=1, q=1)\n",
|
|
"res = am.fit(disp=\"off\")\n",
|
|
"\n",
|
|
"# Extract calibrated parameters\n",
|
|
"mu_fit = res.params[\"mu\"]\n",
|
|
"omega_fit = res.params[\"omega\"]\n",
|
|
"alpha_fit = res.params[\"alpha[1]\"]\n",
|
|
"beta_fit = res.params[\"beta[1]\"]\n",
|
|
"\n",
|
|
"print(\"Calibrated GARCH(1,1) parameters:\")\n",
|
|
"print(f\" mu (mean): {mu_fit:.6f}% daily\")\n",
|
|
"print(f\" omega: {omega_fit:.6f}\")\n",
|
|
"print(f\" alpha (news): {alpha_fit:.4f}\")\n",
|
|
"print(f\" beta (memory): {beta_fit:.4f}\")\n",
|
|
"print(f\" persistence: {alpha_fit + beta_fit:.4f}\")\n",
|
|
"print(f\" unconditional vol: {np.sqrt(omega_fit / (1 - alpha_fit - beta_fit)):.4f}% daily\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f75a6f6d",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.010706,
|
|
"end_time": "2026-06-13T03:11:53.451772+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.441066+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Simulate from Calibrated Parameters\n",
|
|
"\n",
|
|
"Now we can simulate new paths using the fitted parameters."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"id": "c8f48027",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.468403Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.468219Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.472965Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.472224Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.010815,
|
|
"end_time": "2026-06-13T03:11:53.473315+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.462500+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def simulate_garch(\n",
|
|
" n_steps: int,\n",
|
|
" mu: float,\n",
|
|
" omega: float,\n",
|
|
" alpha: float,\n",
|
|
" beta: float,\n",
|
|
" sigma0: float | None = None,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> tuple[np.ndarray, np.ndarray]:\n",
|
|
" \"\"\"\n",
|
|
" Generate GARCH(1,1) return series with mean.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" n_steps : int\n",
|
|
" Number of time steps\n",
|
|
" mu : float\n",
|
|
" Mean return (same units as omega)\n",
|
|
" omega : float\n",
|
|
" Base variance (intercept)\n",
|
|
" alpha : float\n",
|
|
" Shock coefficient (news impact)\n",
|
|
" beta : float\n",
|
|
" Persistence coefficient\n",
|
|
" sigma0 : float, optional\n",
|
|
" Initial volatility. If None, use unconditional volatility.\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" tuple[np.ndarray, np.ndarray]\n",
|
|
" Returns and volatility paths\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" # Unconditional variance\n",
|
|
" uncond_var = omega / (1 - alpha - beta)\n",
|
|
" if sigma0 is None:\n",
|
|
" sigma0 = np.sqrt(uncond_var)\n",
|
|
"\n",
|
|
" returns = np.zeros(n_steps)\n",
|
|
" sigma = np.zeros(n_steps)\n",
|
|
" sigma[0] = sigma0\n",
|
|
"\n",
|
|
" for t in range(n_steps):\n",
|
|
" # Generate return with mean\n",
|
|
" eps = rng.standard_normal()\n",
|
|
" returns[t] = mu + sigma[t] * eps\n",
|
|
"\n",
|
|
" # Update volatility for next period\n",
|
|
" if t < n_steps - 1:\n",
|
|
" shock = returns[t] - mu # Deviation from mean\n",
|
|
" sigma[t + 1] = np.sqrt(omega + alpha * shock**2 + beta * sigma[t] ** 2)\n",
|
|
"\n",
|
|
" return returns, sigma"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "74f141c0",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.004063,
|
|
"end_time": "2026-06-13T03:11:53.481714+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.477651+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### GARCH Simulation from Calibrated Parameters\n",
|
|
"\n",
|
|
"Use the fitted SPY parameters to generate a synthetic path and compare\n",
|
|
"the resulting moments with the calibrated values."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"id": "f14a7371",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.490550Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.490355Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.497827Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.497106Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.012292,
|
|
"end_time": "2026-06-13T03:11:53.498316+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.486024+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"GARCH simulation (calibrated to SPY): 505 prices\n",
|
|
"Simulated annual return: 15.02%\n",
|
|
"Simulated annual vol: 15.8%\n",
|
|
"Excess kurtosis: 2.6772\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Simulate using calibrated parameters\n",
|
|
"garch_rng = np.random.default_rng(46)\n",
|
|
"garch_log_returns_pct, garch_vol = simulate_garch(\n",
|
|
" n_steps=504,\n",
|
|
" mu=mu_fit,\n",
|
|
" omega=omega_fit,\n",
|
|
" alpha=alpha_fit,\n",
|
|
" beta=beta_fit,\n",
|
|
" rng=garch_rng,\n",
|
|
")\n",
|
|
"\n",
|
|
"# Convert to prices (from log returns in percent)\n",
|
|
"garch_log_returns = garch_log_returns_pct / 100 # Convert to decimal log returns\n",
|
|
"garch_prices = 100 * np.exp(np.cumsum(np.insert(garch_log_returns, 0, 0)))\n",
|
|
"\n",
|
|
"print(f\"GARCH simulation (calibrated to SPY): {len(garch_prices)} prices\")\n",
|
|
"print(f\"Simulated annual return: {garch_log_returns.mean() * 252:.2%}\")\n",
|
|
"print(f\"Simulated annual vol: {garch_log_returns.std() * np.sqrt(252):.1%}\")\n",
|
|
"print(f\"Excess kurtosis: {kurtosis(garch_log_returns, fisher=True, bias=False):.4f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e7a226fc",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.004267,
|
|
"end_time": "2026-06-13T03:11:53.507124+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.502857+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: GARCH"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"id": "9e770b4a",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.514986Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.514856Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.529787Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.529237Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.019749,
|
|
"end_time": "2026-06-13T03:11:53.530275+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.510526+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mRate limiter initialized \u001b[0m \u001b[36mmax_calls\u001b[0m=\u001b[35m1000\u001b[0m \u001b[36mperiod\u001b[0m=\u001b[35m1.0\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session initialized \u001b[0m \u001b[36mmax_connections\u001b[0m=\u001b[35m10\u001b[0m \u001b[36mtimeout\u001b[0m=\u001b[35m30.0\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1mdebug \u001b[0m] \u001b[1mHTTP session closed \u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mFetching OHLCV data \u001b[0m \u001b[36mend\u001b[0m=\u001b[35m2023-12-31\u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mstart\u001b[0m=\u001b[35m2022-01-01\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mGenerating 520 synthetic bars \u001b[0m \u001b[36mfrequency\u001b[0m=\u001b[35mdaily\u001b[0m \u001b[36mmodel\u001b[0m=\u001b[35mgarch\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"\u001b[2m2026-06-12 23:11:53\u001b[0m [\u001b[32m\u001b[1minfo \u001b[0m] \u001b[1mSuccessfully fetched OHLCV data\u001b[0m \u001b[36mname\u001b[0m=\u001b[35mSyntheticProvider\u001b[0m \u001b[36mprovider\u001b[0m=\u001b[35msynthetic\u001b[0m \u001b[36mrows\u001b[0m=\u001b[35m520\u001b[0m \u001b[36msymbol\u001b[0m=\u001b[35mSYNTH\u001b[0m\n"
|
|
]
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"SyntheticProvider GARCH: 520 bars, final close=59.49\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"provider = SyntheticProvider(\n",
|
|
" model=\"garch\",\n",
|
|
" garch_omega=omega_fit,\n",
|
|
" garch_alpha=alpha_fit,\n",
|
|
" garch_beta=beta_fit,\n",
|
|
" seed=46,\n",
|
|
")\n",
|
|
"df = provider.fetch_ohlcv(\"SYNTH\", \"2022-01-01\", \"2023-12-31\", \"daily\")\n",
|
|
"print(f\"SyntheticProvider GARCH: {len(df)} bars, final close={float(df['close'][-1]):.2f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1faabacf",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.004646,
|
|
"end_time": "2026-06-13T03:11:53.539724+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.535078+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"---\n",
|
|
"## Visualize All Parametric Models"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"id": "05fc8874",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.551505Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.551256Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:53.553950Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:53.553381Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.009222,
|
|
"end_time": "2026-06-13T03:11:53.554510+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.545288+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Collect all simulations\n",
|
|
"all_models = {\n",
|
|
" \"GBM\": gbm_prices,\n",
|
|
" \"Jump-Diffusion\": jd_prices,\n",
|
|
" \"Mean-Reversion\": mr_prices,\n",
|
|
" \"Heston\": heston_prices,\n",
|
|
" \"GARCH\": garch_prices,\n",
|
|
"}"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 23,
|
|
"id": "54ad6865",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:53.565530Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:53.565374Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:54.529026Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:54.528086Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.970092,
|
|
"end_time": "2026-06-13T03:11:54.529511+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:53.559419+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
".venv/lib/python3.14/site-packages/plotly/io/_base_renderers.py:123: DeprecationWarning: \n",
|
|
"Support for Kaleido versions less than 1.0.0 is deprecated and will be removed after September 2025.\n",
|
|
"Please upgrade Kaleido to version 1.0.0 or greater (`pip install 'kaleido>=1.0.0'` or `pip install 'plotly[kaleido]'`).\n",
|
|
"\n",
|
|
" image_bytes = to_image(\n",
|
|
".venv/lib/python3.14/site-packages/kaleido/scopes/base.py:188: DeprecationWarning: setDaemon() is deprecated, set the daemon attribute instead\n",
|
|
" self._std_error_thread.setDaemon(True)\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"application/vnd.plotly.v1+json": {
|
|
"config": {
|
|
"plotlyServerURL": "https://plot.ly"
|
|
},
|
|
"data": [
|
|
{
|
|
"line": {
|
|
"color": "#0a1628"
|
|
},
|
|
"mode": "lines",
|
|
"name": "GBM",
|
|
"showlegend": false,
|
|
"type": "scatter",
|
|
"xaxis": "x",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#D4A84B"
|
|
},
|
|
"mode": "lines",
|
|
"name": "Jump-Diffusion",
|
|
"showlegend": false,
|
|
"type": "scatter",
|
|
"xaxis": "x2",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y2"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#C87533"
|
|
},
|
|
"mode": "lines",
|
|
"name": "Mean-Reversion",
|
|
"showlegend": false,
|
|
"type": "scatter",
|
|
"xaxis": "x3",
|
|
"y": {
|
|
"bdata": "AwAAAAAAWUAWVo5vsVdZQPm/jYw+XVlArZfFxn9wWUAPcajkn7VZQGrpINZp51lA3HxVTMYJWkCLnNSj5O9ZQAelRb2crllABR53yIbEWUBOj3anP6NZQPQPixU71VlADu7iG63gWUBdB8lsk7BZQEJmS/S/v1lAT4cxlFjqWUBdwswDjfNZQC9/HhHawFlAWJApPpnPWUCgTtopKuRZQOovALXvFVpAsh2xYDZBWkBoHo5XbAVaQD5xpKow5FlAEvYV+zwIWkB1Ue1VgZxZQB1zZZFhy1lAB3qCpMuVWUAnYSZUp3pZQPRz2jrf0llAInb1DyvNWUBiUcsUybhZQKapMnnDyFlAKqUy3VHBWUBKcP04DZlZQDCIkb1Ap1lAfnPJq0wrWkCCtys+GGNaQLDRCCAZfFpAZ0DV3W+JWkBuXnEqablaQEBCQyMW3lpAwkWg4faiWkCNHqaVJsBaQLEWfIzav1pAzpjiaJ4rW0DcBcNdPxlbQOjh1Sn9ZltATU+etxEWW0D4AqyZHSZbQK5s7iw881pAzvVeuW+2WkAgO+OIj+VaQBpPwf8yolpAg2rfm++VWkA/V8oB1WVaQGogsOokfFpAQSifdciKWkCQGjtPmP5ZQLSEU/CYKFpA01Mwaer/WUA4BSo1yXxaQAEVh2lUslpAwbXjTZDsWkBHbWeUrVFaQFPliqQGv1pA1x6dzrG/WkCWnnMzyWhaQO8YAhEFe1pAM/svhkTLWkDidPZPt2RaQE1mOJ8fplpATGH0gNOPWkA8XfVSr2paQLENsCT6TlpAmQJSYqIaWkDw1NsGKCZaQHeiwLagNFpArUwYwCR0WkDjnCcWVMpaQDqPsvq7s1pA+PXRRpT1WkBvOBTyealaQAjMCndnz1pABtGtLAiIWkDq6UK6EWNaQAVmQQUEh1pABwuhpiVXWkDnXvyn6HNaQMY0oBwfGFpA3PZoE4LrWUCshiTHFwtaQN0RL4kqZlpAP4ziT+4cWkClhuS0lHxaQMHwTqqdilpAzccXqzsWW0BjHPV/X/9aQD4THyP621pAoaodmC7tWkAarvNnCaZaQHGAQvIRq1pAwvdIlDKkWkDMrttKa/RaQMfnTy15BltAlzz7d/ezWkBX0WtmjF9aQCijsTpWIlpAQ6YcfJSjWUCrznj8ESNZQET30RQSoVlAQsfhGm5uWUCr9vAoU7tZQC9+H0upjVlACDk1crl0WUAnL3pc6A5ZQKXYmBg/WllAZf+HhbBCWUD5jmQhraZZQOvxUjepe1lApEh6M/DIWUDzX1Qf/iJaQO+PekFKxVlA2Fvu4wTgWUBsZ4V6HaBZQI2slj7NWVlAXD4UF7JgWUCxXx3tL5FZQBws+3OG4llA2qBMQynMWUBuIzw6mwdaQIoJICt2KFpAcblAU5YlWkB4zy1MC+lZQMNWDUTA6VlAolUrFJvDWkBMTkEs7YRaQGNvrVoCd1pAqYJYUwU8WkD67+D/j49aQKUdXFcA/1pAE47hHBlRW0B6gOVGzM1bQMXBuSiAwltAxbq1vsMrXEBY7RyCmu1bQKgJzvfwTlxAQcK8+F+sXEDOBMKwgXlcQBQ1GDTHsVxA45aLsuNfXEDRn6Ym4PlbQGaQ4NGplltA3/MTsjNIW0BxELmTwfhaQOWVFYqe7FpAcrnOBp1YW0C0Lgx0DEJbQMpjiwsrBVtABIaKavUrW0AyRlavLxZbQJbUBR2OFltAjUno2qkqW0BGsTVaT0FbQEsIXWasDltAAIfsYB35WkBuq1hPNjBbQKnFHh3cEVtAsVcSOJf8WkDp8pSt7wpbQKfdG8iwIFtAN02YbU0GW0BucU1oQiVbQH06aib8HltAuAYt3mbEWkCcmVVGNulaQJU8/fPuq1pAkZY1TXBuW0BAzI5tMntbQBzsmBU5YltAO6OZ0UaUW0Br9UHse+9bQOJTtl6cTlxAR3lsATtbXEAZUDuLc5xcQCc8FgFnxFxASnZtDbLBXECcaqQE+VBcQB218JixSlxATfk1ajOWW0DP6IWOeVVbQNZosU4LqltAsoRhX6WvW0CcBTMDa6ZbQGxeICRMZltA+0dMvHEoW0DncGmfn/ZaQKhJLoEjmFpATC0qLkUEWkAy7T1aYEJaQDr7u6JpqFpASnnV7WF7WkBvkI7anKhaQBVeNqa1VVpAVjY7rV5oWkCgh9tpFA1aQMgx8KVlQ1pAAk4F7kRDWkCOQtZil+9ZQNhMplYhD1pAcal/7HR0WkBWoTn33HBaQCEo8zxSalpA/Dp/pB9nWkB/xWj9OmtaQDILYnNSt1pAQVTgnlYGW0BM1EFmMHlaQD+pcQOgwlpAcv0ledmwWkCImONBURhbQGrPFYUEMVtAtuM65LZqW0AiXgklskJbQOxfpLOC5VpAh5m+ExfwWkB1EncE3ilbQI8YYA+cVFtA5rV/bF6CW0DoWtTs94pbQKLeKVZbtFtAS3ZYNJ52W0C6wTeLymZbQGnYBYOE+lpAGvP9orTxWkAGKffBWthaQE1eEHbK1lpA1Gu6VZkVW0B/QPAqLRRbQOPxaeWbU1pA1wYo4E2nWkAQNknAiqxaQIJsxKAJ2lpANS4WBeqhWkDCtVFnsdJaQC7kOFmfMVtA4hI8A5TCWkCkn/3Phw1bQF+fcO1Jy1pAg8w6lMqUWkAnbsWqbpBaQOd4O04KE1tA1LVTmWyYWkCnzEWuDmtaQNF3mICbaVpAS5Xt+SqPWkD0g9fheINaQFq84iyxmlpAbroXwAVUWkAg5SyoaYFaQF1uwx7wwFpAhpFLnEZ1WkBfGSCa8D5aQIilVtJ1VFpAkaGDptJlWkBlAv+FroNaQFHg+DmiMVpAQQIioEkVWkBlhog/K/NZQJNBX7EFRlpAa9AwJm48WkAfQDWb8xhaQJPiZjKx3FlAbaIRKA3aWUDEY3HkiiJaQD43o6iovVlAFCHVYXLCWUAO+F4B5d9ZQM1yhXBOW1pAgiqFQ0KDWkDrgkRz29ZaQIWK6BkA1VpAhj2BHVt2WkAqV18EqxdaQEOJv+oc51lAeaIg1t3sWUAcCi3u9tdZQNsXVfoLuFlA0yeob6AnWkBtiNHp441ZQLdB5UUBS1lAPBgXii7eWUB9l+AA1e5ZQPdInDLMwVlA+l2aS1x5WUAMPx/dc6lZQJO0C8PZ0llAm3HHtzkDWkBDixnWt65ZQHMl+2i9tFlA+QWMBIikWUAcQVyb3r1ZQFuPHaP9VllA9zLjewV6WUA7MGMZ0NdZQB6odoWWf1lA1C+RKxW0WUBq7bOXLhtaQGpeIzyJUFpAnnw+G/FJWkDM4WPZ4U5aQKmbl7+fKVpAPh51dag0WkCY4xWojO9ZQOABGNGG8FlAgrLUgDC5WUBEMw9Y9lxZQI2e8QYkuVlAXPSPNhREWUDr5tv9F7JZQKEN9cZEKVlA0qWoI1ViWUCpSI1W7GxZQHk/KHtFCFlACQ9lvQrpWEA9z3IEUatYQOg8PL+nclhA5BeHiVmoWEA23jAObGJYQH5P0Szx8VdArh1Nsl81WEAFs+LI001YQHBj6t8kT1hAe4cUtYU/WEC0sT4wMmpYQDNx44RkgVhAHWZ6s1x7WECWsi9nAFlYQPp32k6XmlhAlc1L/E7zWECtOIbVBhBZQCDTBFrcyVlArjDJn37WWUBoqQ49f+BZQHVLoTB8P1pAz0rB09xPWkDHof8nCV5aQE19PZdJRFpADai4Q5NgWkA/vkCzIvJZQMAomUAcwllA8/kMauF8WUDCXRG6FvVYQJDbzKUnOFlAhWuW+lMjWUAVsj1kHO1YQN5g9zNzBFlA0Y7j6ai4WECTIA0nye9YQNuiEspuRllAe46+4AXuWEBTgCzGEjdZQK4ka5FTQ1lAcyV6slaJWUD7c1zeupRZQAVXnOr1XllAvVOf4Pn7WED9d1xmfLhYQOKrtJvUmlhAkuFeN4rbWEAmAXEiugJZQD8KnmFfFVlA5oFX2AdwWUClbMsSwv1YQGIUtf2DtlhACNBhQXdyWEAjVyKYzndYQFy27uIsFlhAqjGYN9n1V0B+2y3IxUhYQPAT6bIWhlhAgbiBUeDkWEBiGV3oBsNYQHlqbb/JhVhAfHydB1GXWEDq2peXRGFYQK7s8A+hXVhAHxJl3VJXWEC0OJKbDnlYQOOl4W1X0VhAykr8uQcnWUDys/QkOGFZQFoE+mFzVFlAwQwlS5R9WUBFT0kKxGVZQIp8MipkLVlATELxH9nQWEAAU+9fWa9YQHnBkVE/z1hA6yFmu1D6WEDECTmn/f1YQCNJRbW7IllA9DW7qQABWUDhsnt20mhZQOmWdgaqcllAtRye/D1fWUBQqkRoP4lZQGLOZsEFgFlAmU5w0ISVWUB3gr1lYvNZQBteDuc5wFlAXSN15iSvWUDn6nJxj6RZQCoRUFBkqFlAFutfTUghWkCo5BbBultaQF7oOWZksFpA1qqd7XoLWkCdWrOyhixaQDJS2ZSPP1pA9pEYR35jWkBf2t6h4mVaQJ0aUXF0PFpADV99+a1rWkCtA1vgNWBaQPNTbpYVYVpAqTweqfE7WkAWF/TLVDBaQAfkv2ypU1pAqiCUwHKJWkBFWx7D8YdaQMPoc2wnjlpAiqBxxsGBWkCQBzrlNLxaQCuFqs8yoFpAN3XSUJ+NWkCTeNkmCZVaQGtnIGPEeVpAq4tVmkSNWkBLclvc3vhaQNbjzx/991pAWl0yqQZZW0CrufeEfpZbQJqHIP2ioVtA5nwwwW3PW0CBwFkplTBcQBmB9u/H9FtASgPmpJsjXECn+KsddHdcQAAyouI5QlxAnXvDtWOdXEAa84MTGslcQNM3bp8IjlxAPfJ0Fr+rXEC5SCNqHkdcQJ6GTf6i8VtAg1KpAXuKW0AJdUZS15pbQGqVZIwkgFtAYngc/QJMW0BUmbPdkidbQIZoSwd0IFtAB1xaWtUIW0AaE8rlheZaQD6lWOOC71pA2RNuO+ivWkAFZ6w4yYtaQLdYi5H81VpAdEEXryrrWkAvG5H+bHRaQDqpdHXx11pAeEGd9PmeWkBgBkGUhQlbQGpTC7YMDltAAEqFzNtLW0BAqsXey9RaQBjPYFSaoFpATQU7mUt1WkCEf+ROnk9aQJ6XO3FDHFpAS8OTlRvzWUB0E0wsVepZQKrooEfkwllA/GpTXau4WUC1fA1EXsxZQH+At6qcXVlAqDGRg71OWUAnbUWmUBNZQCF7lB9vDVlAwW3Y+G8yWUDLT8jWuN1YQOKq6AnyxlhAm91sMrL+WEDam7oiOT5ZQMvwTIjcHVlAicPgghFUWUBTVIqpoGVZQEmKtEViaFlAqNF37xJJWUCnefrNRVlZQJVaIo5UgllAV0wKrNhYWUCqBMHs+XRZQCBQcND3LVlA8EE8hanmWEA=",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y3"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#334155"
|
|
},
|
|
"mode": "lines",
|
|
"name": "Heston",
|
|
"showlegend": false,
|
|
"type": "scatter",
|
|
"xaxis": "x4",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y4"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#10b981"
|
|
},
|
|
"mode": "lines",
|
|
"name": "GARCH",
|
|
"showlegend": false,
|
|
"type": "scatter",
|
|
"xaxis": "x5",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y5"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#0a1628"
|
|
},
|
|
"mode": "lines",
|
|
"name": "GBM",
|
|
"type": "scatter",
|
|
"xaxis": "x6",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y6"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#D4A84B"
|
|
},
|
|
"mode": "lines",
|
|
"name": "Jump-Diffusion",
|
|
"type": "scatter",
|
|
"xaxis": "x6",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y6"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#C87533"
|
|
},
|
|
"mode": "lines",
|
|
"name": "Mean-Reversion",
|
|
"type": "scatter",
|
|
"xaxis": "x6",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y6"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#334155"
|
|
},
|
|
"mode": "lines",
|
|
"name": "Heston",
|
|
"type": "scatter",
|
|
"xaxis": "x6",
|
|
"y": {
|
|
"bdata": "AAAAAAAAWUDdIPXhvvZYQCWQPtepH1lATLSrBb83WUA46jjsIEJZQARYNyvJkVlA4MTx8KdxWUC6eGI+HYtZQGyPp5KEcVlAFH43BFGXWUBF21tIfMtZQLHvUn/6rFlAsdk7cTvQWUB/G7JQCIRZQLdjoqyE31lA7nTHch7cWUB7xGTzTNNZQEV5U+w3lVlA5t8FCi24WUBojatjm61ZQDImV60ClVlAgDlHmHgGWkAjXw6lEOhZQEBOJt8JLFpAcYviM2NdWkAObrDJZ0taQLGe6h95mlpA9IxH7t3DWkB6tAugWdlaQKYio0+t01pAVC0P+li8WkC0SGGw5WpaQERq0XOsjFpA7GZzk4UmWkBTIYAMj81ZQBzzz+LBO1pA25F9g1pnWkB/VaI/mFdaQLSKXfo5b1pAQ4PFhh2cWkAO3RFS9b5aQBJMpvOD1FpAbrvPSo/PWkADcP+Tm/daQK6EvRgoG1tA3BlUQmzvWkAm1udQ4OlaQMB+ZyoI/FpA00uRl1iqWkDuv+hR655aQEad37diHFtAIwUzBXIjW0CbIHR4xB5bQL087Qrhz1pAV2kyPYaDWkBBWul7vUpaQG2saADv7lpAFBKM/3qxWkCMPr0v0B5bQHK+Hzi2mVtAid4xg7TaW0Cbh6tWKzxcQCPaB8l6IFxADCuWBGwQXEBmqt2nyOFbQDMIdEGHO1xAjzd9X9VQXEAhySMy7ClcQKqTRDy3WFxAw6gt3MlWXEBY+TBpmJFcQMqAJt8U2FtA/+NaPZagW0Am7s/WgOVbQCbeVzkZSFxAPasSfRz9W0B674lIwIRcQMGUYqGD11xA1I1CDUUOXUCY6nonuzBdQFShgkNB8FxAT8BY6atvXUADuJUpIrFdQA5ydT9r5V1AsrMjXwRlXkABCfavK15eQEP8EiVwkl5AmnnSzUPzXkBUInqzbA1fQJKG83C6GV9AHZfLBXXxXkBFwdtjlR5fQBSXaGS0Nl9AjeEKOZiMXkCmB0pNnZBeQLRCbZvX0V5AGntAFKbrXkBdj/jYB25fQOyQ3JqRp19ABA2MV1qUX0BoGZUz5OJfQO8MYHyaOWBASOUif2UdYEDnqjW8LztgQBC2JbvYNGBAPEJf3KdLYEBVm4VWkUFgQEPz8g0Cc2BAv3F/SBhyYEDcj7tgfmlgQFTLAb0/WGBAhxSyEHaIYEAY/3EZULZgQOnfG9r/1mBAl2xxgk3lYEDdl6rB7e9gQMIL1v0B3WBAk0FAJsQEYUDAsED4aD5hQNoVOyODG2FAqhjsm7RpYUC7fTaUzlxhQMMKZO/6NmFAbF4aNflUYUArndVQX15hQCXTH1u9SWFA66qKxZZ3YUBsXnldKWthQHCXfrannGFA924ieRa3YUDgRL/SMdFhQAuX3jwm7WFAB3LjrbnTYUANOtqOhNthQF6r92B55GFAglRoAVLuYUBKC2XTsvVhQPKTuKoj/GFA/fT7Qb8PYkBmDgk+HBpiQLiRkFIDRWJAP14GUlBMYkB6bmq4MGdiQK/H1MG9PGJAclIRFcVWYkAYSOAplFtiQN4w+GS/rWJAvOKgHiLNYkC+V50TELdiQKhh6qL0tmJA1phSaL65YkBDrMzgPbliQFdRj9VyxWJAViPjV5LJYkCzwW/7YL1iQCmwjEQ0zmJAEYdPPWj0YkCFaoLWf85iQMaOdim2vGJATyrXBeWkYkDVoB7FPqliQKlbRh/f3GJAGscEtEHUYkBiO21PTuFiQM4RA0x4LmNAUkKLydwPY0BzY1kgUzRjQKJZ61oYO2NAiN1yTWQxY0AKfFCjWmBjQJn1OZKTT2NAp6Sb6a0jY0BD/BoDfNxiQCAB9T42/2JAOncZHPUYY0ApPUwfxlFjQA+TksvwM2NA8kaOx8ICY0Dns+dRpexiQAskDGsCymJAQz3Tml/cYkD9r7WCH0hjQBZhHqT/E2NArCqbDdngYkB0PDsoRb1iQGvBjeBTc2JAXQYnMBFlYkALx/3BQOphQDZtNZdv9GFALaDtB+O5YUBhPrPqTnJhQEKFi6aNd2FAOfu98r27YUCiu2eoyMFhQIFYeCWVumFACf2YQoX5YUAUMc8RQlRiQOX33nDlcWJA676QhhgNYkAJ70QvcyNiQP3V68cuOGJAI9IZ2k1WYkDWvgJgSlFiQEN/afLXemJA7amjeRpcYkCIuOfOQppiQHxTtLxX32JAJGfMnYY+Y0Ai6nwfcWpjQH71pAIneGNAFKdY5SmvY0ADSQr8aHtjQGiFOIP9/WNAkflRjp0VZEBBRM0cSD1kQAOg/+4zbGRAqrAZLBnjY0CGJLPqQWNjQFcBeoBI92JAztKKEMTfYkCDqDoZ8KRiQChvFM69bWJASRzE27PkYUBqGpsBefNhQFft14AkEmJAii/wjlrkYUB82M7S27NhQGUEcuPSeGFAYd/eOrRgYUBft0vdamthQGC5LaSFo2FAIl76J2uQYUBDg449/VBhQDW4vG6timFA2nl/n+dpYUC9Hy6yrH9hQOK1bsGi42BAHxwt4xZwYEDn4eHloItgQPU1ZesEgWBAjNoe5733X0D4dhFS6yxgQPuza0vaA2BAInpN5nESYEDP4ll1HdFfQEci+QB4JmBAtVbg3cmQYEAZibzwCnlgQD79BYMcsmBAsSR/wU9hYEDkcZDLyWNgQEy9jJ5bmGBAEf9uHdZ/YEAXlt188HxgQLEN58dCcGBAegpf/uFbYEC6QnBG7VVgQKpWKsRCM2BAIcFhN7NZYEAB2UhwULdgQC0eWi8RymBAPpu7U32+YEAYmANvuXRgQItkFLvBXmBAmLCuZmgLYECH5tk9PVdgQAXoxXJBSWBA3yoQFUJFYED1vGqJeylgQGVbe0+QR2BA94TiXeGFYECFQn2krThgQJK6r+WOSmBAliMPFxR+YEAxnQC2AsVgQCztB7zUwGBAPUuTfySYYEBjZuqrkQFhQAtRiDNhhWBAvgToF4aqYEC1uxh3A9hgQP5mG4MuC2FAKR0/JByZYEDBTO5v8YNgQEkduowbp2BACv2STXvNYED5XsEjVdxgQM2+d7JDt2BASUNijp2gYEDLvm5zm39gQKnV8Y4JzGBALG67UgYDYUAWHL7nofVgQMXqAOTJuGBA62DZD2DiYEAdBY1BRPhgQCedXy7TBmFAi6vEpj2vYEDwPb8jHORgQELxP5U+0WBAhSYmi+jwYEA7b10sltxgQEOlKAmD5mBA9B+dPgTbYEA5PlYgcfZgQJdGE+bj+mBAh6QDkVnOYEAHQjIIZ9dgQP1sMuxr+mBAwBkiEDZlYEB/w1YEq1xgQPRk6zvKrGBA1hV9xcCVYEANnrW/ogFhQPGY4uDQ5GBAWDRhn6u9YECxSog3uQFhQMs4k5Zat2BAhXlP2ysZYUCgzo/c6NJgQBCsC48bqGBAuc3dYENTYEDeSTwy5j9gQF2CVxwza2BArAG3X3r4X0BUZx7EEjJgQJyLD+zMm19AE14qHH/7XkA3JoxYqBJfQDdzRZgvGF9AePbXzOv7XkAuo7xVhq1eQI9zHSlCu15AzWTirgxtXkBUuayMG+ZeQGb2zOZY+l1AIe5I5Tw7XkCYUrmTgbJeQF3CHkpdol5AjVn2E3O9XUBUXBSFU4NdQBS2sKY0al1AcekSSnJ1XUAxVJ6+E+lcQMavoPwkzFtAfXT+4O8FW0BT5w7N8JxbQOwm3RXSOltAE7z8YB3LWkC33QqgL0xZQCZ+96NdgFhAduUouQ7KWEAdHs0nRoVZQEZAJ3JRWVlAg0RtSpOIWUAhS5eUCf5YQKFMR3cgw1hALb5tUpVgWUD3bdpFYOdYQH+avqiqX1hA+DgPZFAfWEBk8pj7I+xYQAqk1bTqZlhAz4zX0hiVV0AMbD2swRVYQOMal9AsUVhARnlXeoFAWECEMg5o9OxXQGYC5CrQGFhAlBSlwwpHWEA38xyQ2xBYQANsiYUQg1hAvfvppjG0WEDmEY0lgv9YQOwIFGYf6FhAOGKw0R9zWEB6Fv9R4K1XQApliTdW0ldAA6bananhV0DyFWB5BXxXQJ9h1LaSjFdACVSFE5d5WECodf4oRp5YQJdUm0yM81hAdpSVcgeLWUBA3XgskANZQN3CHHkBaFlA/bEdMEEYWUA8tK7D6VlZQAqDePfpA1lA6BQ5mgB8WEDXAQB9kShYQINVGcKc7FdAKHGQ698cWEDpOIz3x2FYQJwhrWy/61hAF0QuDOrBWEBux2EaTI9YQH2VhYj9hlhAWFc6833LWEDqhSS/1aRYQLIfMR49nlhAxqP7K9OxWEA41EJezTJZQOFefi9eDVlA7wdQTp9oWUAs3iE2tq9ZQNSy1WBMlVlA7ugG17UwWkCGPjuHsUdaQNpc1fSjqVpA/HBViQbgWkCK3W/4xBlbQJ2WS7Z0CFtAPVBXyQAOW0BKAyJnCNZaQOEg220BzFpAHPI0t19lWkAso8RO9XxaQOyurDhIbVpAwSC3XK+8WkCPT+r941RaQIw5eljbBVpA7JBjOcDUWUBdvLfF3bRZQAVgnwvkXFpAGIXA8P8UWkCAFFWb+OJZQIwWwJmNt1lAZrU0za6/WUA8rRZYI55ZQIbYBqNSt1lAPKRlj4u1WUCaXAvtRWFZQMbaN9KPp1lARFpwyK+nWUAcFY5cJShZQFKQKGZnC1lAWlWQTOFiWEBpWLkhAPhYQCHLVd1uL1lAW6eW9Id7WUCEDFU/he5ZQLbhoYKWdlpAhDKHy6UrWkAlOQJhRj1aQBQjbVo5VVpAnb1WO/vCWkDmBAcefedaQLpdZWx87lpAKVbdcuzRWkDaHzUUSutaQIiPbKdjLltA5M7kct0sW0AW0Anu2jNbQKREIsNHUltAwPIY2wYQW0CD6IUVNMtaQMUKTQu+Z1pAHTRvnVmfWkBxoJrG3N1aQEytUdV7s1pA8p1jMBPYWkAd8znU2uBaQPrmIeecBFtAmu3RH2mPWkCWh9UeszZaQIV+7H4vaVpAGF9pQ666WUBJMC02LEBZQDQlUEEDGllAd9vJYhnRWEBa7WUb2ZZYQA8GvrPCnFhArVfz3jz8WED6n/7I0yBZQOPTpWhloFhABv1N29bVWED7giajhy1ZQAgHE4Uo51hAtjRlox7NWEBDOhHt2GFZQFhQfDmMk1lAOwLv9Xp2WUBhJ3HJTpFZQDpjmx/7BVpAqThUwQTKWUCI8vSD4+VZQI22e49xXlpA6rDEOvtAWkBdvDhNeSRaQEisrLFNTlpA5v6VnFVJWkDDbOtczm1aQLvqgmpFkFpAinYGo+g9WkDo0wc10T9aQLKdC4SigVpAIdMrk26rWkAsFKUTMAFbQInEndSEvVpA/Tg2xKUWW0CyHguzoENbQOOPPLvDXltA3aLs1TH9WkA=",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y6"
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#10b981"
|
|
},
|
|
"mode": "lines",
|
|
"name": "GARCH",
|
|
"type": "scatter",
|
|
"xaxis": "x6",
|
|
"y": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
},
|
|
"yaxis": "y6"
|
|
}
|
|
],
|
|
"layout": {
|
|
"annotations": [
|
|
{
|
|
"font": {
|
|
"size": 16
|
|
},
|
|
"showarrow": false,
|
|
"text": "GBM",
|
|
"x": 0.14444444444444446,
|
|
"xanchor": "center",
|
|
"xref": "paper",
|
|
"y": 1.0,
|
|
"yanchor": "bottom",
|
|
"yref": "paper"
|
|
},
|
|
{
|
|
"font": {
|
|
"size": 16
|
|
},
|
|
"showarrow": false,
|
|
"text": "Jump-Diffusion",
|
|
"x": 0.5,
|
|
"xanchor": "center",
|
|
"xref": "paper",
|
|
"y": 1.0,
|
|
"yanchor": "bottom",
|
|
"yref": "paper"
|
|
},
|
|
{
|
|
"font": {
|
|
"size": 16
|
|
},
|
|
"showarrow": false,
|
|
"text": "Mean-Reversion",
|
|
"x": 0.8555555555555556,
|
|
"xanchor": "center",
|
|
"xref": "paper",
|
|
"y": 1.0,
|
|
"yanchor": "bottom",
|
|
"yref": "paper"
|
|
},
|
|
{
|
|
"font": {
|
|
"size": 16
|
|
},
|
|
"showarrow": false,
|
|
"text": "Heston",
|
|
"x": 0.14444444444444446,
|
|
"xanchor": "center",
|
|
"xref": "paper",
|
|
"y": 0.44,
|
|
"yanchor": "bottom",
|
|
"yref": "paper"
|
|
},
|
|
{
|
|
"font": {
|
|
"size": 16
|
|
},
|
|
"showarrow": false,
|
|
"text": "GARCH",
|
|
"x": 0.5,
|
|
"xanchor": "center",
|
|
"xref": "paper",
|
|
"y": 0.44,
|
|
"yanchor": "bottom",
|
|
"yref": "paper"
|
|
},
|
|
{
|
|
"font": {
|
|
"size": 16
|
|
},
|
|
"showarrow": false,
|
|
"text": "Combined (Normalized)",
|
|
"x": 0.8555555555555556,
|
|
"xanchor": "center",
|
|
"xref": "paper",
|
|
"y": 0.44,
|
|
"yanchor": "bottom",
|
|
"yref": "paper"
|
|
}
|
|
],
|
|
"height": 600,
|
|
"template": {
|
|
"data": {
|
|
"bar": [
|
|
{
|
|
"error_x": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"error_y": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"marker": {
|
|
"line": {
|
|
"color": "white",
|
|
"width": 0.5
|
|
},
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "bar"
|
|
}
|
|
],
|
|
"barpolar": [
|
|
{
|
|
"marker": {
|
|
"line": {
|
|
"color": "white",
|
|
"width": 0.5
|
|
},
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "barpolar"
|
|
}
|
|
],
|
|
"carpet": [
|
|
{
|
|
"aaxis": {
|
|
"endlinecolor": "#2a3f5f",
|
|
"gridcolor": "#C8D4E3",
|
|
"linecolor": "#C8D4E3",
|
|
"minorgridcolor": "#C8D4E3",
|
|
"startlinecolor": "#2a3f5f"
|
|
},
|
|
"baxis": {
|
|
"endlinecolor": "#2a3f5f",
|
|
"gridcolor": "#C8D4E3",
|
|
"linecolor": "#C8D4E3",
|
|
"minorgridcolor": "#C8D4E3",
|
|
"startlinecolor": "#2a3f5f"
|
|
},
|
|
"type": "carpet"
|
|
}
|
|
],
|
|
"choropleth": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "choropleth"
|
|
}
|
|
],
|
|
"contour": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "contour"
|
|
}
|
|
],
|
|
"contourcarpet": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "contourcarpet"
|
|
}
|
|
],
|
|
"heatmap": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "heatmap"
|
|
}
|
|
],
|
|
"histogram": [
|
|
{
|
|
"marker": {
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "histogram"
|
|
}
|
|
],
|
|
"histogram2d": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "histogram2d"
|
|
}
|
|
],
|
|
"histogram2dcontour": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "histogram2dcontour"
|
|
}
|
|
],
|
|
"mesh3d": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "mesh3d"
|
|
}
|
|
],
|
|
"parcoords": [
|
|
{
|
|
"line": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "parcoords"
|
|
}
|
|
],
|
|
"pie": [
|
|
{
|
|
"automargin": true,
|
|
"type": "pie"
|
|
}
|
|
],
|
|
"scatter": [
|
|
{
|
|
"fillpattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
},
|
|
"type": "scatter"
|
|
}
|
|
],
|
|
"scatter3d": [
|
|
{
|
|
"line": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatter3d"
|
|
}
|
|
],
|
|
"scattercarpet": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattercarpet"
|
|
}
|
|
],
|
|
"scattergeo": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattergeo"
|
|
}
|
|
],
|
|
"scattergl": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattergl"
|
|
}
|
|
],
|
|
"scattermap": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattermap"
|
|
}
|
|
],
|
|
"scattermapbox": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattermapbox"
|
|
}
|
|
],
|
|
"scatterpolar": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterpolar"
|
|
}
|
|
],
|
|
"scatterpolargl": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterpolargl"
|
|
}
|
|
],
|
|
"scatterternary": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterternary"
|
|
}
|
|
],
|
|
"surface": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "surface"
|
|
}
|
|
],
|
|
"table": [
|
|
{
|
|
"cells": {
|
|
"fill": {
|
|
"color": "#EBF0F8"
|
|
},
|
|
"line": {
|
|
"color": "white"
|
|
}
|
|
},
|
|
"header": {
|
|
"fill": {
|
|
"color": "#C8D4E3"
|
|
},
|
|
"line": {
|
|
"color": "white"
|
|
}
|
|
},
|
|
"type": "table"
|
|
}
|
|
]
|
|
},
|
|
"layout": {
|
|
"annotationdefaults": {
|
|
"arrowcolor": "#2a3f5f",
|
|
"arrowhead": 0,
|
|
"arrowwidth": 1
|
|
},
|
|
"autotypenumbers": "strict",
|
|
"coloraxis": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"colorscale": {
|
|
"diverging": [
|
|
[
|
|
0,
|
|
"#8e0152"
|
|
],
|
|
[
|
|
0.1,
|
|
"#c51b7d"
|
|
],
|
|
[
|
|
0.2,
|
|
"#de77ae"
|
|
],
|
|
[
|
|
0.3,
|
|
"#f1b6da"
|
|
],
|
|
[
|
|
0.4,
|
|
"#fde0ef"
|
|
],
|
|
[
|
|
0.5,
|
|
"#f7f7f7"
|
|
],
|
|
[
|
|
0.6,
|
|
"#e6f5d0"
|
|
],
|
|
[
|
|
0.7,
|
|
"#b8e186"
|
|
],
|
|
[
|
|
0.8,
|
|
"#7fbc41"
|
|
],
|
|
[
|
|
0.9,
|
|
"#4d9221"
|
|
],
|
|
[
|
|
1,
|
|
"#276419"
|
|
]
|
|
],
|
|
"sequential": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"sequentialminus": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
]
|
|
},
|
|
"colorway": [
|
|
"#636efa",
|
|
"#EF553B",
|
|
"#00cc96",
|
|
"#ab63fa",
|
|
"#FFA15A",
|
|
"#19d3f3",
|
|
"#FF6692",
|
|
"#B6E880",
|
|
"#FF97FF",
|
|
"#FECB52"
|
|
],
|
|
"font": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"geo": {
|
|
"bgcolor": "white",
|
|
"lakecolor": "white",
|
|
"landcolor": "white",
|
|
"showlakes": true,
|
|
"showland": true,
|
|
"subunitcolor": "#C8D4E3"
|
|
},
|
|
"hoverlabel": {
|
|
"align": "left"
|
|
},
|
|
"hovermode": "closest",
|
|
"mapbox": {
|
|
"style": "light"
|
|
},
|
|
"paper_bgcolor": "white",
|
|
"plot_bgcolor": "white",
|
|
"polar": {
|
|
"angularaxis": {
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": ""
|
|
},
|
|
"bgcolor": "white",
|
|
"radialaxis": {
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"scene": {
|
|
"xaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
},
|
|
"yaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
},
|
|
"zaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
}
|
|
},
|
|
"shapedefaults": {
|
|
"line": {
|
|
"color": "#2a3f5f"
|
|
}
|
|
},
|
|
"ternary": {
|
|
"aaxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
},
|
|
"baxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
},
|
|
"bgcolor": "white",
|
|
"caxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"title": {
|
|
"x": 0.05
|
|
},
|
|
"xaxis": {
|
|
"automargin": true,
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": "",
|
|
"title": {
|
|
"standoff": 15
|
|
},
|
|
"zerolinecolor": "#EBF0F8",
|
|
"zerolinewidth": 2
|
|
},
|
|
"yaxis": {
|
|
"automargin": true,
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": "",
|
|
"title": {
|
|
"standoff": 15
|
|
},
|
|
"zerolinecolor": "#EBF0F8",
|
|
"zerolinewidth": 2
|
|
}
|
|
}
|
|
},
|
|
"title": {
|
|
"text": "Stochastic Models: Price Paths"
|
|
},
|
|
"width": 950,
|
|
"xaxis": {
|
|
"anchor": "y",
|
|
"domain": [
|
|
0.0,
|
|
0.2888888888888889
|
|
]
|
|
},
|
|
"xaxis2": {
|
|
"anchor": "y2",
|
|
"domain": [
|
|
0.35555555555555557,
|
|
0.6444444444444445
|
|
]
|
|
},
|
|
"xaxis3": {
|
|
"anchor": "y3",
|
|
"domain": [
|
|
0.7111111111111111,
|
|
1.0
|
|
]
|
|
},
|
|
"xaxis4": {
|
|
"anchor": "y4",
|
|
"domain": [
|
|
0.0,
|
|
0.2888888888888889
|
|
]
|
|
},
|
|
"xaxis5": {
|
|
"anchor": "y5",
|
|
"domain": [
|
|
0.35555555555555557,
|
|
0.6444444444444445
|
|
]
|
|
},
|
|
"xaxis6": {
|
|
"anchor": "y6",
|
|
"domain": [
|
|
0.7111111111111111,
|
|
1.0
|
|
]
|
|
},
|
|
"yaxis": {
|
|
"anchor": "x",
|
|
"domain": [
|
|
0.56,
|
|
1.0
|
|
]
|
|
},
|
|
"yaxis2": {
|
|
"anchor": "x2",
|
|
"domain": [
|
|
0.56,
|
|
1.0
|
|
]
|
|
},
|
|
"yaxis3": {
|
|
"anchor": "x3",
|
|
"domain": [
|
|
0.56,
|
|
1.0
|
|
]
|
|
},
|
|
"yaxis4": {
|
|
"anchor": "x4",
|
|
"domain": [
|
|
0.0,
|
|
0.44
|
|
]
|
|
},
|
|
"yaxis5": {
|
|
"anchor": "x5",
|
|
"domain": [
|
|
0.0,
|
|
0.44
|
|
]
|
|
},
|
|
"yaxis6": {
|
|
"anchor": "x6",
|
|
"domain": [
|
|
0.0,
|
|
0.44
|
|
]
|
|
}
|
|
}
|
|
},
|
|
"image/png": "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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Create comparison plot\n",
|
|
"fig = make_subplots(\n",
|
|
" rows=2,\n",
|
|
" cols=3,\n",
|
|
" subplot_titles=list(all_models.keys()) + [\"Combined (Normalized)\"],\n",
|
|
" vertical_spacing=0.12,\n",
|
|
")\n",
|
|
"\n",
|
|
"colors = [COLORS[\"blue\"], COLORS[\"amber\"], COLORS[\"copper\"], COLORS[\"neutral\"], COLORS[\"positive\"]]\n",
|
|
"\n",
|
|
"# Individual plots (no legend - subplot titles identify each)\n",
|
|
"for idx, (name, prices) in enumerate(all_models.items()):\n",
|
|
" row, col = (idx // 3) + 1, (idx % 3) + 1\n",
|
|
" fig.add_trace(\n",
|
|
" go.Scatter(\n",
|
|
" y=prices, mode=\"lines\", name=name, line=dict(color=colors[idx]), showlegend=False\n",
|
|
" ),\n",
|
|
" row=row,\n",
|
|
" col=col,\n",
|
|
" )\n",
|
|
"\n",
|
|
"# Combined normalized plot (with legend for comparison)\n",
|
|
"for idx, (name, prices) in enumerate(all_models.items()):\n",
|
|
" normalized = 100 * prices / prices[0]\n",
|
|
" fig.add_trace(\n",
|
|
" go.Scatter(y=normalized, mode=\"lines\", name=name, line=dict(color=colors[idx])),\n",
|
|
" row=2,\n",
|
|
" col=3,\n",
|
|
" )\n",
|
|
"\n",
|
|
"fig.update_layout(\n",
|
|
" title_text=\"Stochastic Models: Price Paths\",\n",
|
|
" height=600,\n",
|
|
" width=950,\n",
|
|
" template=\"plotly_white\",\n",
|
|
")\n",
|
|
"fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2feb942e",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.006609,
|
|
"end_time": "2026-06-13T03:11:54.542398+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.535789+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Normalized Price Paths (Grayscale-Compatible)\n",
|
|
"\n",
|
|
"A matplotlib companion to the plotly grid above, using distinct line styles\n",
|
|
"that remain distinguishable in grayscale print."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"id": "a6553aa5",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:54.560797Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:54.560627Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:54.714037Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:54.713543Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.166115,
|
|
"end_time": "2026-06-13T03:11:54.715382+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.549267+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"/tmp/ipykernel_1822063/2517849336.py:51: UserWarning: The figure layout has changed to tight\n",
|
|
" fig.tight_layout()\n",
|
|
"/tmp/ipykernel_1822063/2517849336.py:52: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
|
|
" fig.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
|
"text/plain": [
|
|
"<Figure size 1200x450 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Line styles for grayscale compatibility - varied grays + distinct patterns\n",
|
|
"LINE_STYLES = [\n",
|
|
" {\"linestyle\": \"-\", \"linewidth\": 1.8, \"color\": \"black\"}, # GBM: solid black\n",
|
|
" {\"linestyle\": \"--\", \"linewidth\": 1.8, \"color\": \"#404040\"}, # Jump-Diffusion: dashed dark gray\n",
|
|
" {\n",
|
|
" \"linestyle\": \"-.\",\n",
|
|
" \"linewidth\": 1.8,\n",
|
|
" \"color\": \"#606060\",\n",
|
|
" }, # Mean-Reversion: dash-dot medium gray\n",
|
|
" {\"linestyle\": \":\", \"linewidth\": 2.2, \"color\": \"#202020\"}, # Heston: dotted near-black (thicker)\n",
|
|
" {\n",
|
|
" \"linestyle\": (0, (5, 2, 1, 2)),\n",
|
|
" \"linewidth\": 1.8,\n",
|
|
" \"color\": \"#808080\",\n",
|
|
" }, # GARCH: long-dash-dot gray\n",
|
|
"]\n",
|
|
"\n",
|
|
"# Create wide-format figure (at least 2:1 aspect ratio). Build and style\n",
|
|
"# in a SINGLE cell so the inline backend does not flush the figure mid-\n",
|
|
"# construction with no title / labels / legend\n",
|
|
"# (feedback_split_cell_figure_bug).\n",
|
|
"fig, ax = plt.subplots(figsize=(12, 4.5))\n",
|
|
"\n",
|
|
"# Plot each model normalized to 100\n",
|
|
"for idx, (name, prices) in enumerate(all_models.items()):\n",
|
|
" normalized = 100 * prices / prices[0]\n",
|
|
" ax.plot(normalized, label=name, **LINE_STYLES[idx])\n",
|
|
"\n",
|
|
"# Styling\n",
|
|
"ax.set_xlabel(\"Trading Days\")\n",
|
|
"ax.set_ylabel(\"Normalized Price (Start = 100)\")\n",
|
|
"ax.set_title(\"Classical Simulation Models: Normalized Price Paths\")\n",
|
|
"\n",
|
|
"# Legend outside plot area to avoid overlap\n",
|
|
"ax.legend(\n",
|
|
" loc=\"upper left\",\n",
|
|
" bbox_to_anchor=(0.01, 0.99),\n",
|
|
" frameon=True,\n",
|
|
" fancybox=False,\n",
|
|
" edgecolor=\"lightgray\",\n",
|
|
" fontsize=9,\n",
|
|
")\n",
|
|
"\n",
|
|
"# Add horizontal reference line at 100\n",
|
|
"ax.axhline(y=100, color=\"gray\", linewidth=0.5, linestyle=\"-\", alpha=0.4)\n",
|
|
"\n",
|
|
"# Despine (seaborn style)\n",
|
|
"sns.despine(ax=ax)\n",
|
|
"\n",
|
|
"# Tight layout\n",
|
|
"fig.tight_layout()\n",
|
|
"fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f41e7820",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.009178,
|
|
"end_time": "2026-06-13T03:11:54.733305+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.724127+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"**Interpretation**: GBM produces the smoothest paths — a direct consequence of\n",
|
|
"continuous diffusion with constant volatility. Jump-diffusion adds sudden\n",
|
|
"discontinuities mimicking flash crashes or earnings surprises. Heston's\n",
|
|
"stochastic volatility creates volatility clustering: calm periods punctuated\n",
|
|
"by turbulent episodes. GARCH captures similar clustering in discrete time,\n",
|
|
"while mean-reversion pulls prices back toward equilibrium. The normalized\n",
|
|
"comparison (bottom right) shows models diverge most during high-volatility\n",
|
|
"regimes — precisely where model choice matters most for risk estimation."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f15fbea3",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.006005,
|
|
"end_time": "2026-06-13T03:11:54.746746+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.740741+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Model Statistics Comparison\n",
|
|
"\n",
|
|
"Compute standardized metrics across all parametric models to quantify how\n",
|
|
"each captures (or fails to capture) empirical stylized facts: fat tails\n",
|
|
"(excess kurtosis), asymmetry (skewness), and drawdown behavior."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"id": "59fdc53d",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:54.758480Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:54.758289Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:54.767123Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:54.766622Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.015329,
|
|
"end_time": "2026-06-13T03:11:54.767458+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.752129+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/html": [
|
|
"<div><style>\n",
|
|
".dataframe > thead > tr,\n",
|
|
".dataframe > tbody > tr {\n",
|
|
" text-align: right;\n",
|
|
" white-space: pre-wrap;\n",
|
|
"}\n",
|
|
"</style>\n",
|
|
"<small>shape: (5, 6)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>model</th><th>annual_return</th><th>annual_volatility</th><th>skewness</th><th>excess_kurtosis</th><th>max_drawdown</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>"GBM"</td><td>0.01889</td><td>0.192158</td><td>0.090925</td><td>-0.063961</td><td>-0.198157</td></tr><tr><td>"Jump-Diffusion"</td><td>0.077968</td><td>0.178969</td><td>-1.517941</td><td>8.187056</td><td>-0.250553</td></tr><tr><td>"Mean-Reversion"</td><td>-0.001983</td><td>0.153284</td><td>-0.008841</td><td>-0.168477</td><td>-0.167625</td></tr><tr><td>"Heston"</td><td>0.038278</td><td>0.198933</td><td>-0.493057</td><td>0.938824</td><td>-0.425039</td></tr><tr><td>"GARCH"</td><td>0.150218</td><td>0.158368</td><td>-0.30055</td><td>2.677197</td><td>-0.173504</td></tr></tbody></table></div>"
|
|
],
|
|
"text/plain": [
|
|
"shape: (5, 6)\n",
|
|
"┌────────────────┬───────────────┬───────────────────┬───────────┬─────────────────┬──────────────┐\n",
|
|
"│ model ┆ annual_return ┆ annual_volatility ┆ skewness ┆ excess_kurtosis ┆ max_drawdown │\n",
|
|
"│ --- ┆ --- ┆ --- ┆ --- ┆ --- ┆ --- │\n",
|
|
"│ str ┆ f64 ┆ f64 ┆ f64 ┆ f64 ┆ f64 │\n",
|
|
"╞════════════════╪═══════════════╪═══════════════════╪═══════════╪═════════════════╪══════════════╡\n",
|
|
"│ GBM ┆ 0.01889 ┆ 0.192158 ┆ 0.090925 ┆ -0.063961 ┆ -0.198157 │\n",
|
|
"│ Jump-Diffusion ┆ 0.077968 ┆ 0.178969 ┆ -1.517941 ┆ 8.187056 ┆ -0.250553 │\n",
|
|
"│ Mean-Reversion ┆ -0.001983 ┆ 0.153284 ┆ -0.008841 ┆ -0.168477 ┆ -0.167625 │\n",
|
|
"│ Heston ┆ 0.038278 ┆ 0.198933 ┆ -0.493057 ┆ 0.938824 ┆ -0.425039 │\n",
|
|
"│ GARCH ┆ 0.150218 ┆ 0.158368 ┆ -0.30055 ┆ 2.677197 ┆ -0.173504 │\n",
|
|
"└────────────────┴───────────────┴───────────────────┴───────────┴─────────────────┴──────────────┘"
|
|
]
|
|
},
|
|
"execution_count": 25,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"def compute_model_stats(prices: np.ndarray, name: str) -> dict:\n",
|
|
" \"\"\"Compute key statistics for a price path using log-returns.\"\"\"\n",
|
|
" log_returns = np.diff(np.log(prices))\n",
|
|
" return {\n",
|
|
" \"model\": name,\n",
|
|
" \"annual_return\": log_returns.mean() * 252,\n",
|
|
" \"annual_volatility\": log_returns.std() * np.sqrt(252),\n",
|
|
" \"skewness\": skew(log_returns),\n",
|
|
" \"excess_kurtosis\": kurtosis(log_returns, fisher=True, bias=False),\n",
|
|
" \"max_drawdown\": np.min(prices / np.maximum.accumulate(prices) - 1),\n",
|
|
" }\n",
|
|
"\n",
|
|
"\n",
|
|
"stats_rows = [compute_model_stats(prices, name) for name, prices in all_models.items()]\n",
|
|
"stats_df = pl.DataFrame(stats_rows)\n",
|
|
"stats_df"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"id": "20c26d91",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:54.779139Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:54.779010Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:54.866585Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:54.866054Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.094368,
|
|
"end_time": "2026-06-13T03:11:54.867413+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.773045+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
".venv/lib/python3.14/site-packages/plotly/io/_base_renderers.py:123: DeprecationWarning: \n",
|
|
"Support for Kaleido versions less than 1.0.0 is deprecated and will be removed after September 2025.\n",
|
|
"Please upgrade Kaleido to version 1.0.0 or greater (`pip install 'kaleido>=1.0.0'` or `pip install 'plotly[kaleido]'`).\n",
|
|
"\n",
|
|
" image_bytes = to_image(\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"application/vnd.plotly.v1+json": {
|
|
"config": {
|
|
"plotlyServerURL": "https://plot.ly"
|
|
},
|
|
"data": [
|
|
{
|
|
"histnorm": "probability density",
|
|
"marker": {
|
|
"color": "#0a1628"
|
|
},
|
|
"name": "GBM",
|
|
"nbinsx": 50,
|
|
"opacity": 0.6,
|
|
"type": "histogram",
|
|
"x": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
}
|
|
},
|
|
{
|
|
"histnorm": "probability density",
|
|
"marker": {
|
|
"color": "#D4A84B"
|
|
},
|
|
"name": "Jump-Diffusion",
|
|
"nbinsx": 50,
|
|
"opacity": 0.6,
|
|
"type": "histogram",
|
|
"x": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
}
|
|
},
|
|
{
|
|
"histnorm": "probability density",
|
|
"marker": {
|
|
"color": "#C87533"
|
|
},
|
|
"name": "Mean-Reversion",
|
|
"nbinsx": 50,
|
|
"opacity": 0.6,
|
|
"type": "histogram",
|
|
"x": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
}
|
|
},
|
|
{
|
|
"histnorm": "probability density",
|
|
"marker": {
|
|
"color": "#334155"
|
|
},
|
|
"name": "Heston",
|
|
"nbinsx": 50,
|
|
"opacity": 0.6,
|
|
"type": "histogram",
|
|
"x": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
}
|
|
},
|
|
{
|
|
"histnorm": "probability density",
|
|
"marker": {
|
|
"color": "#10b981"
|
|
},
|
|
"name": "GARCH",
|
|
"nbinsx": 50,
|
|
"opacity": 0.6,
|
|
"type": "histogram",
|
|
"x": {
|
|
"bdata": "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",
|
|
"dtype": "f8"
|
|
}
|
|
}
|
|
],
|
|
"layout": {
|
|
"barmode": "overlay",
|
|
"template": {
|
|
"data": {
|
|
"bar": [
|
|
{
|
|
"error_x": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"error_y": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"marker": {
|
|
"line": {
|
|
"color": "white",
|
|
"width": 0.5
|
|
},
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "bar"
|
|
}
|
|
],
|
|
"barpolar": [
|
|
{
|
|
"marker": {
|
|
"line": {
|
|
"color": "white",
|
|
"width": 0.5
|
|
},
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "barpolar"
|
|
}
|
|
],
|
|
"carpet": [
|
|
{
|
|
"aaxis": {
|
|
"endlinecolor": "#2a3f5f",
|
|
"gridcolor": "#C8D4E3",
|
|
"linecolor": "#C8D4E3",
|
|
"minorgridcolor": "#C8D4E3",
|
|
"startlinecolor": "#2a3f5f"
|
|
},
|
|
"baxis": {
|
|
"endlinecolor": "#2a3f5f",
|
|
"gridcolor": "#C8D4E3",
|
|
"linecolor": "#C8D4E3",
|
|
"minorgridcolor": "#C8D4E3",
|
|
"startlinecolor": "#2a3f5f"
|
|
},
|
|
"type": "carpet"
|
|
}
|
|
],
|
|
"choropleth": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "choropleth"
|
|
}
|
|
],
|
|
"contour": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "contour"
|
|
}
|
|
],
|
|
"contourcarpet": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "contourcarpet"
|
|
}
|
|
],
|
|
"heatmap": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "heatmap"
|
|
}
|
|
],
|
|
"histogram": [
|
|
{
|
|
"marker": {
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "histogram"
|
|
}
|
|
],
|
|
"histogram2d": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "histogram2d"
|
|
}
|
|
],
|
|
"histogram2dcontour": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "histogram2dcontour"
|
|
}
|
|
],
|
|
"mesh3d": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "mesh3d"
|
|
}
|
|
],
|
|
"parcoords": [
|
|
{
|
|
"line": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "parcoords"
|
|
}
|
|
],
|
|
"pie": [
|
|
{
|
|
"automargin": true,
|
|
"type": "pie"
|
|
}
|
|
],
|
|
"scatter": [
|
|
{
|
|
"fillpattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
},
|
|
"type": "scatter"
|
|
}
|
|
],
|
|
"scatter3d": [
|
|
{
|
|
"line": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatter3d"
|
|
}
|
|
],
|
|
"scattercarpet": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattercarpet"
|
|
}
|
|
],
|
|
"scattergeo": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattergeo"
|
|
}
|
|
],
|
|
"scattergl": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattergl"
|
|
}
|
|
],
|
|
"scattermap": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattermap"
|
|
}
|
|
],
|
|
"scattermapbox": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattermapbox"
|
|
}
|
|
],
|
|
"scatterpolar": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterpolar"
|
|
}
|
|
],
|
|
"scatterpolargl": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterpolargl"
|
|
}
|
|
],
|
|
"scatterternary": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterternary"
|
|
}
|
|
],
|
|
"surface": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "surface"
|
|
}
|
|
],
|
|
"table": [
|
|
{
|
|
"cells": {
|
|
"fill": {
|
|
"color": "#EBF0F8"
|
|
},
|
|
"line": {
|
|
"color": "white"
|
|
}
|
|
},
|
|
"header": {
|
|
"fill": {
|
|
"color": "#C8D4E3"
|
|
},
|
|
"line": {
|
|
"color": "white"
|
|
}
|
|
},
|
|
"type": "table"
|
|
}
|
|
]
|
|
},
|
|
"layout": {
|
|
"annotationdefaults": {
|
|
"arrowcolor": "#2a3f5f",
|
|
"arrowhead": 0,
|
|
"arrowwidth": 1
|
|
},
|
|
"autotypenumbers": "strict",
|
|
"coloraxis": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"colorscale": {
|
|
"diverging": [
|
|
[
|
|
0,
|
|
"#8e0152"
|
|
],
|
|
[
|
|
0.1,
|
|
"#c51b7d"
|
|
],
|
|
[
|
|
0.2,
|
|
"#de77ae"
|
|
],
|
|
[
|
|
0.3,
|
|
"#f1b6da"
|
|
],
|
|
[
|
|
0.4,
|
|
"#fde0ef"
|
|
],
|
|
[
|
|
0.5,
|
|
"#f7f7f7"
|
|
],
|
|
[
|
|
0.6,
|
|
"#e6f5d0"
|
|
],
|
|
[
|
|
0.7,
|
|
"#b8e186"
|
|
],
|
|
[
|
|
0.8,
|
|
"#7fbc41"
|
|
],
|
|
[
|
|
0.9,
|
|
"#4d9221"
|
|
],
|
|
[
|
|
1,
|
|
"#276419"
|
|
]
|
|
],
|
|
"sequential": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"sequentialminus": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
]
|
|
},
|
|
"colorway": [
|
|
"#636efa",
|
|
"#EF553B",
|
|
"#00cc96",
|
|
"#ab63fa",
|
|
"#FFA15A",
|
|
"#19d3f3",
|
|
"#FF6692",
|
|
"#B6E880",
|
|
"#FF97FF",
|
|
"#FECB52"
|
|
],
|
|
"font": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"geo": {
|
|
"bgcolor": "white",
|
|
"lakecolor": "white",
|
|
"landcolor": "white",
|
|
"showlakes": true,
|
|
"showland": true,
|
|
"subunitcolor": "#C8D4E3"
|
|
},
|
|
"hoverlabel": {
|
|
"align": "left"
|
|
},
|
|
"hovermode": "closest",
|
|
"mapbox": {
|
|
"style": "light"
|
|
},
|
|
"paper_bgcolor": "white",
|
|
"plot_bgcolor": "white",
|
|
"polar": {
|
|
"angularaxis": {
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": ""
|
|
},
|
|
"bgcolor": "white",
|
|
"radialaxis": {
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"scene": {
|
|
"xaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
},
|
|
"yaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
},
|
|
"zaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
}
|
|
},
|
|
"shapedefaults": {
|
|
"line": {
|
|
"color": "#2a3f5f"
|
|
}
|
|
},
|
|
"ternary": {
|
|
"aaxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
},
|
|
"baxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
},
|
|
"bgcolor": "white",
|
|
"caxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"title": {
|
|
"x": 0.05
|
|
},
|
|
"xaxis": {
|
|
"automargin": true,
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": "",
|
|
"title": {
|
|
"standoff": 15
|
|
},
|
|
"zerolinecolor": "#EBF0F8",
|
|
"zerolinewidth": 2
|
|
},
|
|
"yaxis": {
|
|
"automargin": true,
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": "",
|
|
"title": {
|
|
"standoff": 15
|
|
},
|
|
"zerolinecolor": "#EBF0F8",
|
|
"zerolinewidth": 2
|
|
}
|
|
}
|
|
},
|
|
"title": {
|
|
"text": "Return Distributions by Model (Log-Returns)"
|
|
},
|
|
"xaxis": {
|
|
"title": {
|
|
"text": "Daily Log-Return"
|
|
}
|
|
},
|
|
"yaxis": {
|
|
"title": {
|
|
"text": "Density"
|
|
}
|
|
}
|
|
}
|
|
},
|
|
"image/png": "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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Return distribution comparison\n",
|
|
"fig = go.Figure()\n",
|
|
"\n",
|
|
"for idx, (name, prices) in enumerate(all_models.items()):\n",
|
|
" log_returns = np.diff(np.log(prices))\n",
|
|
" fig.add_trace(\n",
|
|
" go.Histogram(\n",
|
|
" x=log_returns,\n",
|
|
" name=name,\n",
|
|
" opacity=0.6,\n",
|
|
" nbinsx=50,\n",
|
|
" histnorm=\"probability density\",\n",
|
|
" marker_color=colors[idx],\n",
|
|
" )\n",
|
|
" )\n",
|
|
"\n",
|
|
"fig.update_layout(\n",
|
|
" title=\"Return Distributions by Model (Log-Returns)\",\n",
|
|
" xaxis_title=\"Daily Log-Return\",\n",
|
|
" yaxis_title=\"Density\",\n",
|
|
" barmode=\"overlay\",\n",
|
|
" template=\"plotly_white\",\n",
|
|
")\n",
|
|
"fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "60991802",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.032912,
|
|
"end_time": "2026-06-13T03:11:54.913912+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.881000+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"**Interpretation**: GBM returns are near-Gaussian by construction (zero excess\n",
|
|
"kurtosis). Jump-diffusion and GARCH produce the heaviest tails, closest to\n",
|
|
"the empirical leptokurtosis observed in real markets. Heston generates moderate\n",
|
|
"tail weight through its stochastic volatility channel. Mean-reversion shows a\n",
|
|
"compressed distribution due to its pull toward equilibrium. For risk management\n",
|
|
"(VaR, ES), models that understate kurtosis — like plain GBM — systematically\n",
|
|
"underestimate tail losses."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "63e9c02d",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.006285,
|
|
"end_time": "2026-06-13T03:11:54.926857+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.920572+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"---\n",
|
|
"# Part 3: Bootstrap Methods\n",
|
|
"\n",
|
|
"Bootstrap methods resample historical data rather than assuming a parametric\n",
|
|
"model. They preserve the **empirical distribution** exactly, including fat tails.\n",
|
|
"\n",
|
|
"| Method | Block Size | Preserves Autocorrelation | Best For |\n",
|
|
"|--------|-----------|--------------------------|----------|\n",
|
|
"| **IID Bootstrap** | 1 | No | i.i.d. assumption OK |\n",
|
|
"| **Block Bootstrap** | Fixed | Yes (within blocks) | Time series |\n",
|
|
"| **Stationary Bootstrap** | Random | Yes (smoother) | Financial returns |\n",
|
|
"\n",
|
|
"### Key Trade-off\n",
|
|
"\n",
|
|
"- **Parametric**: Can generate scenarios *beyond* historical range\n",
|
|
"- **Bootstrap**: Preserves empirical distribution *exactly* but limited to observed extremes\n",
|
|
"\n",
|
|
"### Consistency Note\n",
|
|
"\n",
|
|
"We bootstrap **log-returns** to match the parametric models above."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "6b3817b1",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.006527,
|
|
"end_time": "2026-06-13T03:11:54.939455+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.932928+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Load Real Data for Bootstrap"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 27,
|
|
"id": "d5e2f4a0",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:54.952958Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:54.952810Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:54.956597Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:54.956239Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.011432,
|
|
"end_time": "2026-06-13T03:11:54.956968+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.945536+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"SPY log-returns: 5030 observations\n",
|
|
"Mean: 0.000408\n",
|
|
"Std: 0.0122\n",
|
|
"Skewness: -0.3042\n",
|
|
"Excess kurtosis: 14.3458 (Fisher, Gaussian=0)\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Compute log-returns (consistent with parametric models)\n",
|
|
"spy_log_returns = np.diff(np.log(spy_close))\n",
|
|
"\n",
|
|
"print(f\"SPY log-returns: {len(spy_log_returns)} observations\")\n",
|
|
"print(f\"Mean: {spy_log_returns.mean():.6f}\")\n",
|
|
"print(f\"Std: {spy_log_returns.std():.4f}\")\n",
|
|
"print(f\"Skewness: {skew(spy_log_returns):.4f}\")\n",
|
|
"print(\n",
|
|
" f\"Excess kurtosis: {kurtosis(spy_log_returns, fisher=True, bias=False):.4f} (Fisher, Gaussian=0)\"\n",
|
|
")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2a141180",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.006379,
|
|
"end_time": "2026-06-13T03:11:54.969821+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.963442+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## 3.1 IID Bootstrap\n",
|
|
"\n",
|
|
"The simplest resampling method: draw individual returns **with replacement**.\n",
|
|
"\n",
|
|
"### Algorithm\n",
|
|
"\n",
|
|
"```\n",
|
|
"For each bootstrap sample of length T:\n",
|
|
" For t = 1 to T:\n",
|
|
" Draw index i uniformly from {1, ..., N}\n",
|
|
" Set r*_t = r_i (original return i)\n",
|
|
" Return r* = (r*_1, ..., r*_T)\n",
|
|
"```\n",
|
|
"\n",
|
|
"### Properties\n",
|
|
"\n",
|
|
"- **Preserves marginal distribution**: Same histogram as original\n",
|
|
"- **Destroys autocorrelation**: Each draw is independent\n",
|
|
"- **Fast and simple**: No tuning parameters"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 28,
|
|
"id": "9f351086",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:54.983349Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:54.983218Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:54.988341Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:54.987910Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.012925,
|
|
"end_time": "2026-06-13T03:11:54.989011+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:54.976086+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"IID Bootstrap vs Original (log-returns):\n",
|
|
" Mean: 0.000341 vs 0.000408\n",
|
|
" Std: 0.0124 vs 0.0122\n",
|
|
" Skew: -0.6880 vs -0.3042\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"def iid_bootstrap(\n",
|
|
" data: np.ndarray,\n",
|
|
" n_samples: int,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" Generate IID bootstrap sample.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" data : np.ndarray\n",
|
|
" Original data\n",
|
|
" n_samples : int\n",
|
|
" Length of bootstrap sample\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" np.ndarray\n",
|
|
" Bootstrap sample\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
" indices = rng.choice(len(data), size=n_samples, replace=True)\n",
|
|
" return data[indices]\n",
|
|
"\n",
|
|
"\n",
|
|
"# Generate one bootstrap sample\n",
|
|
"iid_rng = np.random.default_rng(50)\n",
|
|
"iid_sample = iid_bootstrap(spy_log_returns, len(spy_log_returns), rng=iid_rng)\n",
|
|
"\n",
|
|
"print(\"IID Bootstrap vs Original (log-returns):\")\n",
|
|
"print(f\" Mean: {iid_sample.mean():.6f} vs {spy_log_returns.mean():.6f}\")\n",
|
|
"print(f\" Std: {iid_sample.std():.4f} vs {spy_log_returns.std():.4f}\")\n",
|
|
"print(f\" Skew: {skew(iid_sample):.4f} vs {skew(spy_log_returns):.4f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9ef3d63f",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.011756,
|
|
"end_time": "2026-06-13T03:11:55.013687+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.001931+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: IID Bootstrap"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"id": "46bfff51",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:55.028354Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:55.028171Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:55.036700Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:55.035998Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.016929,
|
|
"end_time": "2026-06-13T03:11:55.037114+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.020185+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"arch IIDBootstrap (100 samples): mean of means = 0.000400\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"bs = IIDBootstrap(spy_log_returns, seed=50)\n",
|
|
"means = [data[0].mean() for data, _ in bs.bootstrap(100)]\n",
|
|
"print(f\"arch IIDBootstrap (100 samples): mean of means = {np.mean(means):.6f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "bdd83bd0",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.007809,
|
|
"end_time": "2026-06-13T03:11:55.058770+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.050961+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## 3.2 Block Bootstrap\n",
|
|
"\n",
|
|
"Resample **contiguous blocks** of fixed length to preserve local dependence.\n",
|
|
"\n",
|
|
"### Algorithm (Moving Block Bootstrap)\n",
|
|
"\n",
|
|
"```\n",
|
|
"Choose block length b\n",
|
|
"For each bootstrap sample of length T:\n",
|
|
" While sample length < T:\n",
|
|
" Draw start index i uniformly from {1, ..., N-b+1}\n",
|
|
" Append block (r_i, r_{i+1}, ..., r_{i+b-1})\n",
|
|
" Trim to length T\n",
|
|
"```\n",
|
|
"\n",
|
|
"### Block Length Selection\n",
|
|
"\n",
|
|
"- Rule of thumb: $b \\approx T^{1/3}$\n",
|
|
"- Financial: ~22 days (one month) is common\n",
|
|
"- Optimal: Cross-validation on out-of-sample statistics"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 30,
|
|
"id": "06d5be9d",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:55.082929Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:55.082733Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:55.088525Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:55.088046Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.020441,
|
|
"end_time": "2026-06-13T03:11:55.089343+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.068902+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Block Bootstrap (block_size=22) vs Original:\n",
|
|
" Mean: 0.000321 vs 0.000408\n",
|
|
" Std: 0.0127 vs 0.0122\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"def block_bootstrap(\n",
|
|
" data: np.ndarray,\n",
|
|
" block_size: int,\n",
|
|
" n_samples: int,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" Generate moving block bootstrap sample.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" data : np.ndarray\n",
|
|
" Original data\n",
|
|
" block_size : int\n",
|
|
" Fixed block length\n",
|
|
" n_samples : int\n",
|
|
" Length of bootstrap sample\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" np.ndarray\n",
|
|
" Bootstrap sample\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" n = len(data)\n",
|
|
" result = []\n",
|
|
"\n",
|
|
" while len(result) < n_samples:\n",
|
|
" start = rng.integers(0, n - block_size + 1)\n",
|
|
" block = data[start : start + block_size]\n",
|
|
" result.extend(block)\n",
|
|
"\n",
|
|
" return np.array(result[:n_samples])\n",
|
|
"\n",
|
|
"\n",
|
|
"# Generate block bootstrap sample (22-day blocks)\n",
|
|
"block_size = 22\n",
|
|
"block_rng = np.random.default_rng(51)\n",
|
|
"block_sample = block_bootstrap(spy_log_returns, block_size, len(spy_log_returns), rng=block_rng)\n",
|
|
"\n",
|
|
"print(f\"Block Bootstrap (block_size={block_size}) vs Original:\")\n",
|
|
"print(f\" Mean: {block_sample.mean():.6f} vs {spy_log_returns.mean():.6f}\")\n",
|
|
"print(f\" Std: {block_sample.std():.4f} vs {spy_log_returns.std():.4f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1a1def06",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.017775,
|
|
"end_time": "2026-06-13T03:11:55.120392+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.102617+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: Block Bootstrap"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 31,
|
|
"id": "19f7f12b",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:55.143464Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:55.143328Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:55.147614Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:55.147266Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.015233,
|
|
"end_time": "2026-06-13T03:11:55.148171+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.132938+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"arch MovingBlockBootstrap (100 samples): mean of means = 0.000426\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"bs = MovingBlockBootstrap(block_size, spy_log_returns, seed=51)\n",
|
|
"means = [data[0].mean() for data, _ in bs.bootstrap(100)]\n",
|
|
"print(f\"arch MovingBlockBootstrap (100 samples): mean of means = {np.mean(means):.6f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "11722d87",
|
|
"metadata": {
|
|
"lines_to_next_cell": 2,
|
|
"papermill": {
|
|
"duration": 0.008682,
|
|
"end_time": "2026-06-13T03:11:55.166828+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.158146+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## 3.3 Stationary Bootstrap\n",
|
|
"\n",
|
|
"Uses **random block lengths** from a geometric distribution, eliminating\n",
|
|
"artificial block boundaries.\n",
|
|
"\n",
|
|
"### Algorithm (Politis & Romano 1994)\n",
|
|
"\n",
|
|
"```\n",
|
|
"Choose expected block length b\n",
|
|
"For each bootstrap sample of length T:\n",
|
|
" Set t = 0\n",
|
|
" While t < T:\n",
|
|
" Draw start index i uniformly from {1, ..., N}\n",
|
|
" Draw block length L from Geometric(1/b)\n",
|
|
" Append (r_i, r_{i+1}, ..., r_{i+L-1}) with wrap-around\n",
|
|
" t = t + L\n",
|
|
" Trim to length T\n",
|
|
"```\n",
|
|
"\n",
|
|
"### Why \"Stationary\"?\n",
|
|
"\n",
|
|
"With random block lengths, the bootstrap distribution is **stationary** -\n",
|
|
"each position in the sample has the same marginal distribution."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 32,
|
|
"id": "68331a09",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:55.209037Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:55.208922Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:55.216307Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:55.215851Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.038119,
|
|
"end_time": "2026-06-13T03:11:55.217250+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.179131+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Stationary Bootstrap (expected block=22) vs Original:\n",
|
|
" Mean: 0.000413 vs 0.000408\n",
|
|
" Std: 0.0111 vs 0.0122\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"def stationary_bootstrap(\n",
|
|
" data: np.ndarray,\n",
|
|
" expected_block_size: float,\n",
|
|
" n_samples: int,\n",
|
|
" rng: np.random.Generator | None = None,\n",
|
|
") -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" Generate stationary bootstrap sample.\n",
|
|
"\n",
|
|
" Parameters\n",
|
|
" ----------\n",
|
|
" data : np.ndarray\n",
|
|
" Original data\n",
|
|
" expected_block_size : float\n",
|
|
" Expected block length (geometric distribution parameter)\n",
|
|
" n_samples : int\n",
|
|
" Length of bootstrap sample\n",
|
|
" rng : np.random.Generator, optional\n",
|
|
" Random number generator\n",
|
|
"\n",
|
|
" Returns\n",
|
|
" -------\n",
|
|
" np.ndarray\n",
|
|
" Bootstrap sample\n",
|
|
" \"\"\"\n",
|
|
" if rng is None:\n",
|
|
" rng = np.random.default_rng()\n",
|
|
"\n",
|
|
" n = len(data)\n",
|
|
" p = 1.0 / expected_block_size # Probability of ending block\n",
|
|
" result = []\n",
|
|
"\n",
|
|
" while len(result) < n_samples:\n",
|
|
" pos = rng.integers(0, n)\n",
|
|
"\n",
|
|
" while len(result) < n_samples:\n",
|
|
" result.append(data[pos])\n",
|
|
" pos = (pos + 1) % n # Wrap around\n",
|
|
"\n",
|
|
" if rng.random() < p:\n",
|
|
" break\n",
|
|
"\n",
|
|
" return np.array(result[:n_samples])\n",
|
|
"\n",
|
|
"\n",
|
|
"# Generate stationary bootstrap sample\n",
|
|
"stat_rng = np.random.default_rng(52)\n",
|
|
"stat_sample = stationary_bootstrap(spy_log_returns, block_size, len(spy_log_returns), rng=stat_rng)\n",
|
|
"\n",
|
|
"print(f\"Stationary Bootstrap (expected block={block_size}) vs Original:\")\n",
|
|
"print(f\" Mean: {stat_sample.mean():.6f} vs {spy_log_returns.mean():.6f}\")\n",
|
|
"print(f\" Std: {stat_sample.std():.4f} vs {spy_log_returns.std():.4f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "615b60bc",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.01474,
|
|
"end_time": "2026-06-13T03:11:55.255148+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.240408+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Library Usage: Stationary Bootstrap"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 33,
|
|
"id": "4f4eb619",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:55.274528Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:55.274410Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:55.282090Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:55.281460Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.017913,
|
|
"end_time": "2026-06-13T03:11:55.282520+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.264607+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"arch StationaryBootstrap (100 samples): mean of means = 0.000401\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"bs = StationaryBootstrap(block_size, spy_log_returns, seed=52)\n",
|
|
"means = [data[0].mean() for data, _ in bs.bootstrap(100)]\n",
|
|
"print(f\"arch StationaryBootstrap (100 samples): mean of means = {np.mean(means):.6f}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c91fc919",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.008196,
|
|
"end_time": "2026-06-13T03:11:55.300411+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.292215+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Bootstrap Method Comparison"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 34,
|
|
"id": "ceaea0e6",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:55.314921Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:55.314770Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:55.321013Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:55.320521Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.013505,
|
|
"end_time": "2026-06-13T03:11:55.321372+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.307867+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/html": [
|
|
"<div><style>\n",
|
|
".dataframe > thead > tr,\n",
|
|
".dataframe > tbody > tr {\n",
|
|
" text-align: right;\n",
|
|
" white-space: pre-wrap;\n",
|
|
"}\n",
|
|
"</style>\n",
|
|
"<small>shape: (4, 5)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>method</th><th>mean</th><th>std</th><th>skew</th><th>excess_kurtosis</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>"Original"</td><td>0.000408</td><td>0.01222</td><td>-0.304239</td><td>14.345821</td></tr><tr><td>"IID"</td><td>0.000341</td><td>0.012435</td><td>-0.687978</td><td>12.397964</td></tr><tr><td>"Block"</td><td>0.000321</td><td>0.012722</td><td>0.251989</td><td>18.360753</td></tr><tr><td>"Stationary"</td><td>0.000413</td><td>0.011101</td><td>-0.446737</td><td>13.644643</td></tr></tbody></table></div>"
|
|
],
|
|
"text/plain": [
|
|
"shape: (4, 5)\n",
|
|
"┌────────────┬──────────┬──────────┬───────────┬─────────────────┐\n",
|
|
"│ method ┆ mean ┆ std ┆ skew ┆ excess_kurtosis │\n",
|
|
"│ --- ┆ --- ┆ --- ┆ --- ┆ --- │\n",
|
|
"│ str ┆ f64 ┆ f64 ┆ f64 ┆ f64 │\n",
|
|
"╞════════════╪══════════╪══════════╪═══════════╪═════════════════╡\n",
|
|
"│ Original ┆ 0.000408 ┆ 0.01222 ┆ -0.304239 ┆ 14.345821 │\n",
|
|
"│ IID ┆ 0.000341 ┆ 0.012435 ┆ -0.687978 ┆ 12.397964 │\n",
|
|
"│ Block ┆ 0.000321 ┆ 0.012722 ┆ 0.251989 ┆ 18.360753 │\n",
|
|
"│ Stationary ┆ 0.000413 ┆ 0.011101 ┆ -0.446737 ┆ 13.644643 │\n",
|
|
"└────────────┴──────────┴──────────┴───────────┴─────────────────┘"
|
|
]
|
|
},
|
|
"execution_count": 34,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Collect bootstrap samples\n",
|
|
"bootstrap_samples = {\n",
|
|
" \"Original\": spy_log_returns,\n",
|
|
" \"IID\": iid_sample,\n",
|
|
" \"Block\": block_sample,\n",
|
|
" \"Stationary\": stat_sample,\n",
|
|
"}\n",
|
|
"\n",
|
|
"# Compare moments\n",
|
|
"bootstrap_stats = []\n",
|
|
"for name, sample in bootstrap_samples.items():\n",
|
|
" bootstrap_stats.append(\n",
|
|
" {\n",
|
|
" \"method\": name,\n",
|
|
" \"mean\": sample.mean(),\n",
|
|
" \"std\": sample.std(),\n",
|
|
" \"skew\": skew(sample),\n",
|
|
" \"excess_kurtosis\": kurtosis(sample, fisher=True, bias=False),\n",
|
|
" }\n",
|
|
" )\n",
|
|
"\n",
|
|
"pl.DataFrame(bootstrap_stats)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ff46e9ad",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.007683,
|
|
"end_time": "2026-06-13T03:11:55.337430+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.329747+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Autocorrelation Preservation\n",
|
|
"\n",
|
|
"The key difference between bootstrap methods is how they handle **temporal\n",
|
|
"dependence**. We measure this via autocorrelation of **squared returns**\n",
|
|
"(signature of volatility clustering)."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 35,
|
|
"id": "efef8424",
|
|
"metadata": {
|
|
"execution": {
|
|
"iopub.execute_input": "2026-06-13T03:11:55.351144Z",
|
|
"iopub.status.busy": "2026-06-13T03:11:55.351006Z",
|
|
"iopub.status.idle": "2026-06-13T03:11:55.426897Z",
|
|
"shell.execute_reply": "2026-06-13T03:11:55.426132Z"
|
|
},
|
|
"papermill": {
|
|
"duration": 0.083647,
|
|
"end_time": "2026-06-13T03:11:55.427488+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.343841+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
".venv/lib/python3.14/site-packages/plotly/io/_base_renderers.py:123: DeprecationWarning: \n",
|
|
"Support for Kaleido versions less than 1.0.0 is deprecated and will be removed after September 2025.\n",
|
|
"Please upgrade Kaleido to version 1.0.0 or greater (`pip install 'kaleido>=1.0.0'` or `pip install 'plotly[kaleido]'`).\n",
|
|
"\n",
|
|
" image_bytes = to_image(\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"application/vnd.plotly.v1+json": {
|
|
"config": {
|
|
"plotlyServerURL": "https://plot.ly"
|
|
},
|
|
"data": [
|
|
{
|
|
"line": {
|
|
"color": "#0a1628"
|
|
},
|
|
"mode": "lines+markers",
|
|
"name": "Original",
|
|
"type": "scatter",
|
|
"x": [
|
|
0,
|
|
1,
|
|
2,
|
|
3,
|
|
4,
|
|
5,
|
|
6,
|
|
7,
|
|
8,
|
|
9,
|
|
10,
|
|
11,
|
|
12,
|
|
13,
|
|
14,
|
|
15,
|
|
16,
|
|
17,
|
|
18,
|
|
19,
|
|
20
|
|
],
|
|
"y": {
|
|
"bdata": "AAAAAAAA8D8v12IClXTRP27W4sk72dw/egAruwjNzz/7uAuwx6/SP96gQHgjT9M/euj1pL2f0T8t95B8Ap7RPxdpfeq9hsw/U62gJoRo0T+IUek1whTPPz57S7mnudM/RAAkOiTlyD+Xrq+pi1bGP72ViOQ1n74/HHskBA13xD+EpPLo1CzIP8MsUuDydsc/Y7IcZXcexj/Gm7alj9bAPytke1phz8I/",
|
|
"dtype": "f8"
|
|
}
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#D4A84B"
|
|
},
|
|
"mode": "lines+markers",
|
|
"name": "IID",
|
|
"type": "scatter",
|
|
"x": [
|
|
0,
|
|
1,
|
|
2,
|
|
3,
|
|
4,
|
|
5,
|
|
6,
|
|
7,
|
|
8,
|
|
9,
|
|
10,
|
|
11,
|
|
12,
|
|
13,
|
|
14,
|
|
15,
|
|
16,
|
|
17,
|
|
18,
|
|
19,
|
|
20
|
|
],
|
|
"y": {
|
|
"bdata": "AAAAAAAA8D+tXvdcn4dhP1/0hbo3UWi/ObCqRvGnMr9WqbLxJTF3v30ctoOshZE/pXNseeFLjD/hIDQoXKqHv1sXYe2YRIa/Lzc7/cHmSj+z8BDcsuQqPxVLWbN5L5W/X8lHLFBghr8XCg/5blZtv2J3G8MweIu/D/ocCzlvkr/+we4o3UA+v0Tt9JHorJe/d00kXuPjaD/6v9C/7XZRP5KwodEgu3m/",
|
|
"dtype": "f8"
|
|
}
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#C87533"
|
|
},
|
|
"mode": "lines+markers",
|
|
"name": "Block",
|
|
"type": "scatter",
|
|
"x": [
|
|
0,
|
|
1,
|
|
2,
|
|
3,
|
|
4,
|
|
5,
|
|
6,
|
|
7,
|
|
8,
|
|
9,
|
|
10,
|
|
11,
|
|
12,
|
|
13,
|
|
14,
|
|
15,
|
|
16,
|
|
17,
|
|
18,
|
|
19,
|
|
20
|
|
],
|
|
"y": {
|
|
"bdata": "AAAAAAAA8D8fzqIl/xHBPxekb6mEht0/jBc9dmG1xT/j3cTIjEzOP/DlrK9QqNA/Ge1zhackxD85K8g1A8/KP7vk8yD3xbg/GPdMIlpJ0T/gHZxGL7e+PwVQMEbM29Q/0TCE5ODEsj/wrnDDPGi/P820XS48Z58/gsTCY6vHrT8yyuhdBaCxP11BRiL1Y5c/qvxZjYh0lD+zJe3cOa+UP+aKYcFFNlU/",
|
|
"dtype": "f8"
|
|
}
|
|
},
|
|
{
|
|
"line": {
|
|
"color": "#334155"
|
|
},
|
|
"mode": "lines+markers",
|
|
"name": "Stationary",
|
|
"type": "scatter",
|
|
"x": [
|
|
0,
|
|
1,
|
|
2,
|
|
3,
|
|
4,
|
|
5,
|
|
6,
|
|
7,
|
|
8,
|
|
9,
|
|
10,
|
|
11,
|
|
12,
|
|
13,
|
|
14,
|
|
15,
|
|
16,
|
|
17,
|
|
18,
|
|
19,
|
|
20
|
|
],
|
|
"y": {
|
|
"bdata": "AAAAAAAA8D9kS2OPpWDDP9sVrgg5fNo/16DVwFkQxj8+h2T21v/IP9/aLJM/Zc4/JgW/PWgzxD8XfZFLHlHKP7PUq7eoUcA/u5JQJ1N6zj8seeGtx4HGP1Fsy7kUEdM/P5uHfSU/wj/Inm0BhdjBP9PHnUR+g64/T3g0rFQutj+slOEpoA66P8U+dXY4vLU/iVaSopZYtj/lodzmOlGyPyxnPBCdu7E/",
|
|
"dtype": "f8"
|
|
}
|
|
}
|
|
],
|
|
"layout": {
|
|
"template": {
|
|
"data": {
|
|
"bar": [
|
|
{
|
|
"error_x": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"error_y": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"marker": {
|
|
"line": {
|
|
"color": "white",
|
|
"width": 0.5
|
|
},
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "bar"
|
|
}
|
|
],
|
|
"barpolar": [
|
|
{
|
|
"marker": {
|
|
"line": {
|
|
"color": "white",
|
|
"width": 0.5
|
|
},
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "barpolar"
|
|
}
|
|
],
|
|
"carpet": [
|
|
{
|
|
"aaxis": {
|
|
"endlinecolor": "#2a3f5f",
|
|
"gridcolor": "#C8D4E3",
|
|
"linecolor": "#C8D4E3",
|
|
"minorgridcolor": "#C8D4E3",
|
|
"startlinecolor": "#2a3f5f"
|
|
},
|
|
"baxis": {
|
|
"endlinecolor": "#2a3f5f",
|
|
"gridcolor": "#C8D4E3",
|
|
"linecolor": "#C8D4E3",
|
|
"minorgridcolor": "#C8D4E3",
|
|
"startlinecolor": "#2a3f5f"
|
|
},
|
|
"type": "carpet"
|
|
}
|
|
],
|
|
"choropleth": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "choropleth"
|
|
}
|
|
],
|
|
"contour": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "contour"
|
|
}
|
|
],
|
|
"contourcarpet": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "contourcarpet"
|
|
}
|
|
],
|
|
"heatmap": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "heatmap"
|
|
}
|
|
],
|
|
"histogram": [
|
|
{
|
|
"marker": {
|
|
"pattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
}
|
|
},
|
|
"type": "histogram"
|
|
}
|
|
],
|
|
"histogram2d": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "histogram2d"
|
|
}
|
|
],
|
|
"histogram2dcontour": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "histogram2dcontour"
|
|
}
|
|
],
|
|
"mesh3d": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"type": "mesh3d"
|
|
}
|
|
],
|
|
"parcoords": [
|
|
{
|
|
"line": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "parcoords"
|
|
}
|
|
],
|
|
"pie": [
|
|
{
|
|
"automargin": true,
|
|
"type": "pie"
|
|
}
|
|
],
|
|
"scatter": [
|
|
{
|
|
"fillpattern": {
|
|
"fillmode": "overlay",
|
|
"size": 10,
|
|
"solidity": 0.2
|
|
},
|
|
"type": "scatter"
|
|
}
|
|
],
|
|
"scatter3d": [
|
|
{
|
|
"line": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatter3d"
|
|
}
|
|
],
|
|
"scattercarpet": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattercarpet"
|
|
}
|
|
],
|
|
"scattergeo": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattergeo"
|
|
}
|
|
],
|
|
"scattergl": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattergl"
|
|
}
|
|
],
|
|
"scattermap": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattermap"
|
|
}
|
|
],
|
|
"scattermapbox": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scattermapbox"
|
|
}
|
|
],
|
|
"scatterpolar": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterpolar"
|
|
}
|
|
],
|
|
"scatterpolargl": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterpolargl"
|
|
}
|
|
],
|
|
"scatterternary": [
|
|
{
|
|
"marker": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"type": "scatterternary"
|
|
}
|
|
],
|
|
"surface": [
|
|
{
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
},
|
|
"colorscale": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"type": "surface"
|
|
}
|
|
],
|
|
"table": [
|
|
{
|
|
"cells": {
|
|
"fill": {
|
|
"color": "#EBF0F8"
|
|
},
|
|
"line": {
|
|
"color": "white"
|
|
}
|
|
},
|
|
"header": {
|
|
"fill": {
|
|
"color": "#C8D4E3"
|
|
},
|
|
"line": {
|
|
"color": "white"
|
|
}
|
|
},
|
|
"type": "table"
|
|
}
|
|
]
|
|
},
|
|
"layout": {
|
|
"annotationdefaults": {
|
|
"arrowcolor": "#2a3f5f",
|
|
"arrowhead": 0,
|
|
"arrowwidth": 1
|
|
},
|
|
"autotypenumbers": "strict",
|
|
"coloraxis": {
|
|
"colorbar": {
|
|
"outlinewidth": 0,
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"colorscale": {
|
|
"diverging": [
|
|
[
|
|
0,
|
|
"#8e0152"
|
|
],
|
|
[
|
|
0.1,
|
|
"#c51b7d"
|
|
],
|
|
[
|
|
0.2,
|
|
"#de77ae"
|
|
],
|
|
[
|
|
0.3,
|
|
"#f1b6da"
|
|
],
|
|
[
|
|
0.4,
|
|
"#fde0ef"
|
|
],
|
|
[
|
|
0.5,
|
|
"#f7f7f7"
|
|
],
|
|
[
|
|
0.6,
|
|
"#e6f5d0"
|
|
],
|
|
[
|
|
0.7,
|
|
"#b8e186"
|
|
],
|
|
[
|
|
0.8,
|
|
"#7fbc41"
|
|
],
|
|
[
|
|
0.9,
|
|
"#4d9221"
|
|
],
|
|
[
|
|
1,
|
|
"#276419"
|
|
]
|
|
],
|
|
"sequential": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
],
|
|
"sequentialminus": [
|
|
[
|
|
0.0,
|
|
"#0d0887"
|
|
],
|
|
[
|
|
0.1111111111111111,
|
|
"#46039f"
|
|
],
|
|
[
|
|
0.2222222222222222,
|
|
"#7201a8"
|
|
],
|
|
[
|
|
0.3333333333333333,
|
|
"#9c179e"
|
|
],
|
|
[
|
|
0.4444444444444444,
|
|
"#bd3786"
|
|
],
|
|
[
|
|
0.5555555555555556,
|
|
"#d8576b"
|
|
],
|
|
[
|
|
0.6666666666666666,
|
|
"#ed7953"
|
|
],
|
|
[
|
|
0.7777777777777778,
|
|
"#fb9f3a"
|
|
],
|
|
[
|
|
0.8888888888888888,
|
|
"#fdca26"
|
|
],
|
|
[
|
|
1.0,
|
|
"#f0f921"
|
|
]
|
|
]
|
|
},
|
|
"colorway": [
|
|
"#636efa",
|
|
"#EF553B",
|
|
"#00cc96",
|
|
"#ab63fa",
|
|
"#FFA15A",
|
|
"#19d3f3",
|
|
"#FF6692",
|
|
"#B6E880",
|
|
"#FF97FF",
|
|
"#FECB52"
|
|
],
|
|
"font": {
|
|
"color": "#2a3f5f"
|
|
},
|
|
"geo": {
|
|
"bgcolor": "white",
|
|
"lakecolor": "white",
|
|
"landcolor": "white",
|
|
"showlakes": true,
|
|
"showland": true,
|
|
"subunitcolor": "#C8D4E3"
|
|
},
|
|
"hoverlabel": {
|
|
"align": "left"
|
|
},
|
|
"hovermode": "closest",
|
|
"mapbox": {
|
|
"style": "light"
|
|
},
|
|
"paper_bgcolor": "white",
|
|
"plot_bgcolor": "white",
|
|
"polar": {
|
|
"angularaxis": {
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": ""
|
|
},
|
|
"bgcolor": "white",
|
|
"radialaxis": {
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"scene": {
|
|
"xaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
},
|
|
"yaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
},
|
|
"zaxis": {
|
|
"backgroundcolor": "white",
|
|
"gridcolor": "#DFE8F3",
|
|
"gridwidth": 2,
|
|
"linecolor": "#EBF0F8",
|
|
"showbackground": true,
|
|
"ticks": "",
|
|
"zerolinecolor": "#EBF0F8"
|
|
}
|
|
},
|
|
"shapedefaults": {
|
|
"line": {
|
|
"color": "#2a3f5f"
|
|
}
|
|
},
|
|
"ternary": {
|
|
"aaxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
},
|
|
"baxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
},
|
|
"bgcolor": "white",
|
|
"caxis": {
|
|
"gridcolor": "#DFE8F3",
|
|
"linecolor": "#A2B1C6",
|
|
"ticks": ""
|
|
}
|
|
},
|
|
"title": {
|
|
"x": 0.05
|
|
},
|
|
"xaxis": {
|
|
"automargin": true,
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": "",
|
|
"title": {
|
|
"standoff": 15
|
|
},
|
|
"zerolinecolor": "#EBF0F8",
|
|
"zerolinewidth": 2
|
|
},
|
|
"yaxis": {
|
|
"automargin": true,
|
|
"gridcolor": "#EBF0F8",
|
|
"linecolor": "#EBF0F8",
|
|
"ticks": "",
|
|
"title": {
|
|
"standoff": 15
|
|
},
|
|
"zerolinecolor": "#EBF0F8",
|
|
"zerolinewidth": 2
|
|
}
|
|
}
|
|
},
|
|
"title": {
|
|
"text": "ACF of Squared Returns: Bootstrap Method Comparison"
|
|
},
|
|
"xaxis": {
|
|
"title": {
|
|
"text": "Lag (days)"
|
|
}
|
|
},
|
|
"yaxis": {
|
|
"title": {
|
|
"text": "Autocorrelation"
|
|
}
|
|
}
|
|
}
|
|
},
|
|
"image/png": "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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Compute ACF for squared returns\n",
|
|
"n_lags = 20\n",
|
|
"fig = go.Figure()\n",
|
|
"\n",
|
|
"bootstrap_colors = [COLORS[\"blue\"], COLORS[\"amber\"], COLORS[\"copper\"], COLORS[\"neutral\"]]\n",
|
|
"\n",
|
|
"for idx, (name, sample) in enumerate(bootstrap_samples.items()):\n",
|
|
" squared = sample**2\n",
|
|
" acf_values = acf(squared, nlags=n_lags, fft=True)\n",
|
|
" fig.add_trace(\n",
|
|
" go.Scatter(\n",
|
|
" x=list(range(n_lags + 1)),\n",
|
|
" y=acf_values,\n",
|
|
" mode=\"lines+markers\",\n",
|
|
" name=name,\n",
|
|
" line=dict(color=bootstrap_colors[idx]),\n",
|
|
" )\n",
|
|
" )\n",
|
|
"\n",
|
|
"fig.update_layout(\n",
|
|
" title=\"ACF of Squared Returns: Bootstrap Method Comparison\",\n",
|
|
" xaxis_title=\"Lag (days)\",\n",
|
|
" yaxis_title=\"Autocorrelation\",\n",
|
|
" template=\"plotly_white\",\n",
|
|
")\n",
|
|
"fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "8a6204e2",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.01002,
|
|
"end_time": "2026-06-13T03:11:55.448586+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.438566+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Bootstrap Key Takeaways\n",
|
|
"\n",
|
|
"1. **IID Bootstrap**: Simple and fast, but **destroys** temporal dependence\n",
|
|
"2. **Block Bootstrap**: Preserves autocorrelation **within** blocks, has boundary artifacts\n",
|
|
"3. **Stationary Bootstrap**: Random blocks = **smoother** preservation of dependence\n",
|
|
"\n",
|
|
"For financial returns with volatility clustering, prefer **Block** or\n",
|
|
"**Stationary** bootstrap. The ACF of squared returns shows preservation quality."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "165c5163",
|
|
"metadata": {
|
|
"papermill": {
|
|
"duration": 0.008208,
|
|
"end_time": "2026-06-13T03:11:55.466958+00:00",
|
|
"exception": false,
|
|
"start_time": "2026-06-13T03:11:55.458750+00:00",
|
|
"status": "completed"
|
|
}
|
|
},
|
|
"source": [
|
|
"---\n",
|
|
"# Part 4: Model Comparison Summary\n",
|
|
"\n",
|
|
"## What Each Method Captures\n",
|
|
"\n",
|
|
"| Method | Fat Tails | Volatility Clustering | Beyond History |\n",
|
|
"|--------|----------|----------------------|----------------|\n",
|
|
"| GBM | No | No | Yes |\n",
|
|
"| Jump-Diffusion | Yes | No | Yes |\n",
|
|
"| Mean-Reversion | No | Negative autocorr | Yes |\n",
|
|
"| Heston | Yes | Yes | Yes |\n",
|
|
"| GARCH | Yes | Yes | Yes |\n",
|
|
"| IID Bootstrap | Yes | No | No |\n",
|
|
"| Block Bootstrap | Yes | Partial | No |\n",
|
|
"| Stationary Bootstrap | Yes | Yes | No |\n",
|
|
"\n",
|
|
"## Key Takeaways\n",
|
|
"\n",
|
|
"1. **Parametric models** (GBM, Jump-Diffusion, Heston, GARCH) can generate scenarios\n",
|
|
" beyond historical experience but require choosing or calibrating parameters\n",
|
|
"2. **Bootstrap methods** (IID, Block, Stationary) preserve the empirical distribution\n",
|
|
" exactly but cannot produce extremes not seen in the original data\n",
|
|
"3. **No classical model captures all stylized facts**: Heston and GARCH come closest\n",
|
|
" with fat tails and volatility clustering, but miss higher-order dependencies\n",
|
|
"4. **Drift compensation** (Jump-Diffusion) and **full truncation** (Heston) are\n",
|
|
" critical implementation details that affect simulation correctness\n",
|
|
"5. **GARCH calibration** via MLE bridges the gap between assumed and observed dynamics,\n",
|
|
" producing more realistic volatility paths than fixed-parameter models\n",
|
|
"\n",
|
|
"**Next**: See [`01_timegan`](01_timegan.ipynb) for the first learned generative model, which uses\n",
|
|
"adversarial training to capture temporal dynamics that classical models miss.\n",
|
|
"\n",
|
|
"**Book**: Chapter 5, Section 5.2 covers the generative model taxonomy and explains\n",
|
|
"why learned models complement (rather than replace) classical simulation."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"jupytext": {
|
|
"formats": "ipynb,py:percent",
|
|
"cell_metadata_filter": "tags,-all"
|
|
},
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.14.3"
|
|
},
|
|
"papermill": {
|
|
"default_parameters": {},
|
|
"duration": 8.96718,
|
|
"end_time": "2026-06-13T03:11:58.091200+00:00",
|
|
"environment_variables": {},
|
|
"exception": null,
|
|
"input_path": "05_synthetic_data/00_classical_simulation.ipynb",
|
|
"output_path": "05_synthetic_data/00_classical_simulation.ipynb",
|
|
"parameters": {},
|
|
"start_time": "2026-06-13T03:11:49.124020+00:00",
|
|
"version": "2.7.0"
|
|
},
|
|
"ml4t_provenance": {
|
|
"source_py_blob": "d51c65cf6f47f594a5647a3fa19d9d6738f096bd",
|
|
"executed_at": "2026-06-13T03:11:58.460461+00:00",
|
|
"executor": "cpu-local",
|
|
"production": true,
|
|
"parameters": {},
|
|
"notes": "executed-state finalization batch (2026-06-13 run)"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|