wehub-resource-sync
11630 lines
663 KiB
Plaintext
11630 lines
663 KiB
Plaintext
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"source": [
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"# Options Greeks: From Theory to Computation\n",
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"\n",
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"**Docker image**: `ml4t`\n",
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"\n",
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"## Purpose\n",
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"\n",
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"Derive Black-Scholes pricing and Greeks from first principles, implement implied\n",
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"volatility via root-finding, and validate the computations against the\n",
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"vendor-supplied values in the AlgoSeek options dataset.\n",
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"\n",
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"## Learning Objectives\n",
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"\n",
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"- Implement Black-Scholes call/put pricing and verify put-call parity.\n",
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"- Solve for implied volatility numerically using Brent's method.\n",
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"- Code all five Greeks (Delta, Gamma, Vega, Theta, Rho) and visualize their\n",
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" behavior across moneyness and time to expiration.\n",
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"- Quantify residuals between in-house and vendor-computed Greeks and explain\n",
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" the residual sources.\n",
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"\n",
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"## Book Reference\n",
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"\n",
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"Chapter 2 §2.2 (asset-class market data landscape — derivatives).\n",
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"\n",
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"## Prerequisites\n",
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"\n",
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"- Basic calculus (partial derivatives) and the standard normal distribution.\n",
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"- Options terminology from `07_sp500_options_eda`.\n",
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"- The AlgoSeek S&P 500 options EDA parquet at `$ML4T_DATA_PATH/equities/market/sp500/options_eda/`."
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]
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"source": [
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"\"\"\"Options Greeks — Black-Scholes pricing, IV computation, and Greeks validation.\"\"\"\n",
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"\n",
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"import numpy as np\n",
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"import plotly.express as px\n",
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"import plotly.graph_objects as go\n",
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"import polars as pl\n",
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"from plotly.subplots import make_subplots\n",
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"from scipy import stats\n",
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"from scipy.optimize import brentq\n",
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"\n",
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"from data import load_sp500_options_eda"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "871b4077",
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},
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"tags": [
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"parameters"
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]
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},
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"outputs": [],
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"source": [
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"# Production defaults\n",
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"RISK_FREE_RATE = 0.015 # 3-month Treasury rate, ~typical pre-COVID 2020\n",
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"N_GREEKS_VALIDATE = 500 # Sample size for Greeks comparison\n",
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"N_IV_VALIDATE = 200 # Sample size for IV recovery comparison"
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]
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"source": [
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"## 1. The Black-Scholes Framework\n",
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"\n",
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"The Black-Scholes model (1973) provides closed-form solutions for European option\n",
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"prices under specific assumptions. Understanding these assumptions is critical for\n",
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"practitioners - model limitations explain many real-world pricing phenomena.\n",
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"\n",
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"### Model Assumptions\n",
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"\n",
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"| Assumption | Reality | Implication |\n",
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"|------------|---------|-------------|\n",
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"| Log-normal returns | Fat tails exist | Underprices tail risk |\n",
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"| Constant volatility | Vol changes over time | Need to re-estimate σ |\n",
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"| No dividends | Stocks pay dividends | Use dividend-adjusted models |\n",
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"| No transaction costs | Costs exist | Greeks less useful for small positions |\n",
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"| Continuous trading | Markets close | Weekend/overnight gaps |\n",
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"| European exercise | Many options are American | Early exercise premium missed |\n",
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"| Constant risk-free rate | Rates vary | Use term-matched rates |\n",
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"\n",
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"Despite these limitations, Black-Scholes remains the industry standard for\n",
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"quoting volatility and computing Greeks. The model's tractability outweighs\n",
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"its theoretical shortcomings for most practical applications."
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]
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"source": [
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"### The Black-Scholes Formula\n",
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"\n",
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"For a European call option:\n",
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"\n",
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"$$C = S \\cdot N(d_1) - K \\cdot e^{-rT} \\cdot N(d_2)$$\n",
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"\n",
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"For a European put option:\n",
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"\n",
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"$$P = K \\cdot e^{-rT} \\cdot N(-d_2) - S \\cdot N(-d_1)$$\n",
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"\n",
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"Where:\n",
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"- $S$ = Current stock price\n",
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"- $K$ = Strike price\n",
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"- $T$ = Time to expiration (in years)\n",
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"- $r$ = Risk-free interest rate\n",
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"- $\\sigma$ = Volatility (annualized standard deviation of log returns)\n",
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"- $N(\\cdot)$ = Cumulative normal distribution function\n",
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"\n",
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"And $d_1$, $d_2$ are:\n",
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"\n",
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"$$d_1 = \\frac{\\ln(S/K) + (r + \\sigma^2/2)T}{\\sigma\\sqrt{T}}$$\n",
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"\n",
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"$$d_2 = d_1 - \\sigma\\sqrt{T}$$"
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]
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"source": [
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"# Small helper functions for d1 and d2 (tightly coupled, <=5 lines each)\n",
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"def d1(S: float, K: float, T: float, r: float, sigma: float) -> float:\n",
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" \"\"\"Compute d1 parameter for Black-Scholes formula.\"\"\"\n",
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" return (np.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))\n",
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"\n",
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"\n",
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"def d2(S: float, K: float, T: float, r: float, sigma: float) -> float:\n",
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" \"\"\"Compute d2 parameter: d2 = d1 - sigma * sqrt(T).\"\"\"\n",
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||
" return d1(S, K, T, r, sigma) - sigma * np.sqrt(T)"
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]
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},
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"source": [
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"### Call Pricing"
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]
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},
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"outputs": [],
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"source": [
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||
"def bs_call_price(S: float, K: float, T: float, r: float, sigma: float) -> float:\n",
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||
" \"\"\"Black-Scholes price for a European call option.\"\"\"\n",
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" if T <= 0:\n",
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" return max(S - K, 0) # Intrinsic value at expiration\n",
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||
" d_1 = d1(S, K, T, r, sigma)\n",
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||
" d_2 = d2(S, K, T, r, sigma)\n",
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||
" return S * stats.norm.cdf(d_1) - K * np.exp(-r * T) * stats.norm.cdf(d_2)"
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]
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},
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},
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"source": [
|
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"### Put Pricing"
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]
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},
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{
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"outputs": [],
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"source": [
|
||
"def bs_put_price(S: float, K: float, T: float, r: float, sigma: float) -> float:\n",
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" \"\"\"Black-Scholes price for a European put option.\"\"\"\n",
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" if T <= 0:\n",
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" return max(K - S, 0) # Intrinsic value at expiration\n",
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" d_1 = d1(S, K, T, r, sigma)\n",
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||
" d_2 = d2(S, K, T, r, sigma)\n",
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||
" return K * np.exp(-r * T) * stats.norm.cdf(-d_2) - S * stats.norm.cdf(-d_1)"
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"source": [
|
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"### Unified Pricing Function"
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]
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"outputs": [],
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"source": [
|
||
"def bs_price(\n",
|
||
" S: float, K: float, T: float, r: float, sigma: float, option_type: str = \"call\"\n",
|
||
") -> float:\n",
|
||
" \"\"\"Black-Scholes option price (call or put).\"\"\"\n",
|
||
" if option_type.lower() == \"call\":\n",
|
||
" return bs_call_price(S, K, T, r, sigma)\n",
|
||
" else:\n",
|
||
" return bs_put_price(S, K, T, r, sigma)"
|
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]
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},
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},
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"source": [
|
||
"### Verify Put-Call Parity\n",
|
||
"\n",
|
||
"A fundamental relationship that must hold for European options:\n",
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||
"\n",
|
||
"$$C - P = S - K \\cdot e^{-rT}$$\n",
|
||
"\n",
|
||
"This provides a sanity check for our implementation."
|
||
]
|
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},
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{
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
||
"=== Black-Scholes Implementation Test ===\n",
|
||
"Parameters: S=100, K=100, T=0.25, r=0.05, σ=0.2\n",
|
||
"\n",
|
||
"Call price: $4.6150\n",
|
||
"Put price: $3.3728\n",
|
||
"\n",
|
||
"Put-Call Parity Check:\n",
|
||
" C - P = 1.242220\n",
|
||
" S - Ke^(-rT) = 1.242220\n",
|
||
" Difference: 7.11e-15\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Test parameters\n",
|
||
"S, K, T, r, sigma = 100, 100, 0.25, 0.05, 0.20\n",
|
||
"\n",
|
||
"call_price = bs_call_price(S, K, T, r, sigma)\n",
|
||
"put_price = bs_put_price(S, K, T, r, sigma)\n",
|
||
"\n",
|
||
"# Put-call parity check\n",
|
||
"lhs = call_price - put_price\n",
|
||
"rhs = S - K * np.exp(-r * T)\n",
|
||
"\n",
|
||
"print(\"=== Black-Scholes Implementation Test ===\")\n",
|
||
"print(f\"Parameters: S={S}, K={K}, T={T}, r={r}, σ={sigma}\")\n",
|
||
"print(f\"\\nCall price: ${call_price:.4f}\")\n",
|
||
"print(f\"Put price: ${put_price:.4f}\")\n",
|
||
"print(\"\\nPut-Call Parity Check:\")\n",
|
||
"print(f\" C - P = {lhs:.6f}\")\n",
|
||
"print(f\" S - Ke^(-rT) = {rhs:.6f}\")\n",
|
||
"print(f\" Difference: {abs(lhs - rhs):.2e}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1a27db13",
|
||
"metadata": {
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.002681,
|
||
"end_time": "2026-06-13T02:33:14.559355+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.556674+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"## 2. Implied Volatility Computation\n",
|
||
"\n",
|
||
"Implied volatility (IV) is the volatility value that, when plugged into\n",
|
||
"Black-Scholes, produces the observed market price. Since there's no closed-form\n",
|
||
"solution, we must solve numerically:\n",
|
||
"\n",
|
||
"$$\\text{Find } \\sigma^* \\text{ such that } BS(S, K, T, r, \\sigma^*) = P_{market}$$\n",
|
||
"\n",
|
||
"We'll use Brent's method (a robust root-finding algorithm) to solve this."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "84b07557",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.564367Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.564280Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:14.566688Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:14.566378Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.005294,
|
||
"end_time": "2026-06-13T02:33:14.566977+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.561683+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def implied_volatility(\n",
|
||
" market_price: float,\n",
|
||
" S: float,\n",
|
||
" K: float,\n",
|
||
" T: float,\n",
|
||
" r: float,\n",
|
||
" option_type: str = \"call\",\n",
|
||
" bounds: tuple = (0.001, 5.0),\n",
|
||
") -> float | None:\n",
|
||
" \"\"\"Compute implied volatility using Brent's method.\n",
|
||
"\n",
|
||
" Returns the volatility that makes BS price equal market_price, or None.\n",
|
||
" \"\"\"\n",
|
||
" if T <= 0:\n",
|
||
" return None\n",
|
||
"\n",
|
||
" # Define objective function: BS_price(sigma) - market_price = 0\n",
|
||
" def objective(sigma):\n",
|
||
" return bs_price(S, K, T, r, sigma, option_type) - market_price\n",
|
||
"\n",
|
||
" try:\n",
|
||
" # Check if solution exists within bounds\n",
|
||
" f_low = objective(bounds[0])\n",
|
||
" f_high = objective(bounds[1])\n",
|
||
"\n",
|
||
" if f_low * f_high > 0:\n",
|
||
" # No sign change - no solution in bounds\n",
|
||
" return None\n",
|
||
"\n",
|
||
" # Brent's method for root finding\n",
|
||
" iv = brentq(objective, bounds[0], bounds[1], xtol=1e-8)\n",
|
||
" return iv\n",
|
||
"\n",
|
||
" except (ValueError, RuntimeError):\n",
|
||
" return None"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "e8e5669a",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.571240Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.571176Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:14.573912Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:14.573549Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.0055,
|
||
"end_time": "2026-06-13T02:33:14.574368+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.568868+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"=== Implied Volatility Test ===\n",
|
||
"Original volatility: 0.2500\n",
|
||
"Generated call price: $5.5984\n",
|
||
"Recovered IV: 0.2500\n",
|
||
"Error: 9.26e-12\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Test IV computation\n",
|
||
"test_vol = 0.25\n",
|
||
"test_call_price = bs_call_price(S, K, T, r, test_vol)\n",
|
||
"\n",
|
||
"recovered_iv = implied_volatility(test_call_price, S, K, T, r, \"call\")\n",
|
||
"\n",
|
||
"print(\"=== Implied Volatility Test ===\")\n",
|
||
"print(f\"Original volatility: {test_vol:.4f}\")\n",
|
||
"print(f\"Generated call price: ${test_call_price:.4f}\")\n",
|
||
"print(f\"Recovered IV: {recovered_iv:.4f}\")\n",
|
||
"print(f\"Error: {abs(test_vol - recovered_iv):.2e}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5392fee5",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.001952,
|
||
"end_time": "2026-06-13T02:33:14.579737+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.577785+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"## 3. The Greeks: Measuring Option Sensitivities\n",
|
||
"\n",
|
||
"Greeks measure how option prices change with respect to various inputs.\n",
|
||
"They're essential for:\n",
|
||
"- **Hedging**: Neutralizing unwanted exposures\n",
|
||
"- **Risk Management**: Understanding portfolio sensitivities\n",
|
||
"- **Trading**: Identifying mispriced options\n",
|
||
"\n",
|
||
"### Summary of Greeks\n",
|
||
"\n",
|
||
"| Greek | Symbol | Measures | Formula |\n",
|
||
"|-------|--------|----------|---------|\n",
|
||
"| Delta | $\\Delta$ | ∂V/∂S | Price sensitivity to underlying |\n",
|
||
"| Gamma | $\\Gamma$ | ∂²V/∂S² | Delta sensitivity to underlying |\n",
|
||
"| Vega | $\\mathcal{V}$ | ∂V/∂σ | Price sensitivity to volatility |\n",
|
||
"| Theta | $\\Theta$ | ∂V/∂t | Price sensitivity to time (decay) |\n",
|
||
"| Rho | $\\rho$ | ∂V/∂r | Price sensitivity to interest rate |"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bc492d20",
|
||
"metadata": {
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.001867,
|
||
"end_time": "2026-06-13T02:33:14.583519+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.581652+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Delta ($\\Delta$)\n",
|
||
"\n",
|
||
"Delta measures the rate of change of option price with respect to the underlying:\n",
|
||
"\n",
|
||
"$$\\Delta_{call} = N(d_1)$$\n",
|
||
"$$\\Delta_{put} = N(d_1) - 1 = -N(-d_1)$$\n",
|
||
"\n",
|
||
"**Interpretation**:\n",
|
||
"- Call delta ranges from 0 to 1\n",
|
||
"- Put delta ranges from -1 to 0\n",
|
||
"- ATM options have |Δ| ≈ 0.5\n",
|
||
"- Delta also approximates probability of finishing ITM"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "14e4760b",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.588109Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.588017Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:14.590206Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:14.589873Z"
|
||
},
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.00504,
|
||
"end_time": "2026-06-13T02:33:14.590470+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.585430+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def delta(S: float, K: float, T: float, r: float, sigma: float, option_type: str = \"call\") -> float:\n",
|
||
" \"\"\"Compute Black-Scholes delta.\"\"\"\n",
|
||
" if T <= 0:\n",
|
||
" if option_type.lower() == \"call\":\n",
|
||
" return 1.0 if S > K else 0.0\n",
|
||
" else:\n",
|
||
" return -1.0 if S < K else 0.0\n",
|
||
"\n",
|
||
" d_1 = d1(S, K, T, r, sigma)\n",
|
||
"\n",
|
||
" if option_type.lower() == \"call\":\n",
|
||
" return stats.norm.cdf(d_1)\n",
|
||
" else:\n",
|
||
" return stats.norm.cdf(d_1) - 1"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "480c67ad",
|
||
"metadata": {
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.001893,
|
||
"end_time": "2026-06-13T02:33:14.594347+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.592454+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Gamma ($\\Gamma$)\n",
|
||
"\n",
|
||
"Gamma measures the rate of change of delta (option's \"acceleration\"):\n",
|
||
"\n",
|
||
"$$\\Gamma = \\frac{N'(d_1)}{S \\sigma \\sqrt{T}}$$\n",
|
||
"\n",
|
||
"Where $N'(x)$ is the standard normal PDF.\n",
|
||
"\n",
|
||
"**Interpretation**:\n",
|
||
"- Gamma is highest for ATM options near expiration\n",
|
||
"- Same for calls and puts (by put-call parity)\n",
|
||
"- High gamma = delta changes rapidly = harder to hedge"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "a8640d73",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.598742Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.598672Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:14.600420Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:14.600141Z"
|
||
},
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.004542,
|
||
"end_time": "2026-06-13T02:33:14.600789+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.596247+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def gamma(S: float, K: float, T: float, r: float, sigma: float) -> float:\n",
|
||
" \"\"\"\n",
|
||
" Compute Black-Scholes gamma (same for calls and puts).\n",
|
||
" \"\"\"\n",
|
||
" if T <= 0:\n",
|
||
" return 0.0\n",
|
||
"\n",
|
||
" d_1 = d1(S, K, T, r, sigma)\n",
|
||
" return stats.norm.pdf(d_1) / (S * sigma * np.sqrt(T))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "da8b7946",
|
||
"metadata": {
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.001882,
|
||
"end_time": "2026-06-13T02:33:14.604611+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.602729+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Vega ($\\mathcal{V}$)\n",
|
||
"\n",
|
||
"Vega measures sensitivity to implied volatility:\n",
|
||
"\n",
|
||
"$$\\mathcal{V} = S \\sqrt{T} \\cdot N'(d_1)$$\n",
|
||
"\n",
|
||
"**Interpretation**:\n",
|
||
"- Usually quoted per 1% change in volatility (divide by 100)\n",
|
||
"- Highest for ATM options with longer time to expiration\n",
|
||
"- Same for calls and puts"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "0ff248f2",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.609278Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.609188Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:14.611141Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:14.610786Z"
|
||
},
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.004807,
|
||
"end_time": "2026-06-13T02:33:14.611369+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.606562+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def vega(S: float, K: float, T: float, r: float, sigma: float) -> float:\n",
|
||
" \"\"\"\n",
|
||
" Compute Black-Scholes vega.\n",
|
||
" Returns vega per 1 point (100%) change in volatility.\n",
|
||
" Divide by 100 for vega per 1% change.\n",
|
||
" \"\"\"\n",
|
||
" if T <= 0:\n",
|
||
" return 0.0\n",
|
||
"\n",
|
||
" d_1 = d1(S, K, T, r, sigma)\n",
|
||
" return S * np.sqrt(T) * stats.norm.pdf(d_1)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9fba2e30",
|
||
"metadata": {
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.001912,
|
||
"end_time": "2026-06-13T02:33:14.615247+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.613335+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Theta ($\\Theta$)\n",
|
||
"\n",
|
||
"Theta measures time decay - how option value erodes as time passes:\n",
|
||
"\n",
|
||
"$$\\Theta_{call} = -\\frac{S \\sigma N'(d_1)}{2\\sqrt{T}} - rKe^{-rT}N(d_2)$$\n",
|
||
"\n",
|
||
"$$\\Theta_{put} = -\\frac{S \\sigma N'(d_1)}{2\\sqrt{T}} + rKe^{-rT}N(-d_2)$$\n",
|
||
"\n",
|
||
"**Interpretation**:\n",
|
||
"- Usually negative (options lose value over time)\n",
|
||
"- Accelerates as expiration approaches\n",
|
||
"- Deep ITM puts can have positive theta"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"id": "c653c9a9",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.619599Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.619533Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:14.621623Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:14.621342Z"
|
||
},
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.004794,
|
||
"end_time": "2026-06-13T02:33:14.621937+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.617143+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def theta(S: float, K: float, T: float, r: float, sigma: float, option_type: str = \"call\") -> float:\n",
|
||
" \"\"\"\n",
|
||
" Compute Black-Scholes theta (per year).\n",
|
||
" Divide by 365 for daily theta.\n",
|
||
" \"\"\"\n",
|
||
" if T <= 0:\n",
|
||
" return 0.0\n",
|
||
"\n",
|
||
" d_1 = d1(S, K, T, r, sigma)\n",
|
||
" d_2 = d2(S, K, T, r, sigma)\n",
|
||
"\n",
|
||
" term1 = -S * sigma * stats.norm.pdf(d_1) / (2 * np.sqrt(T))\n",
|
||
"\n",
|
||
" if option_type.lower() == \"call\":\n",
|
||
" term2 = -r * K * np.exp(-r * T) * stats.norm.cdf(d_2)\n",
|
||
" else:\n",
|
||
" term2 = r * K * np.exp(-r * T) * stats.norm.cdf(-d_2)\n",
|
||
"\n",
|
||
" return term1 + term2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b14c5743",
|
||
"metadata": {
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.001874,
|
||
"end_time": "2026-06-13T02:33:14.625739+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.623865+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Rho ($\\rho$)\n",
|
||
"\n",
|
||
"Rho measures sensitivity to interest rates:\n",
|
||
"\n",
|
||
"$$\\rho_{call} = KTe^{-rT}N(d_2)$$\n",
|
||
"$$\\rho_{put} = -KTe^{-rT}N(-d_2)$$\n",
|
||
"\n",
|
||
"**Interpretation**:\n",
|
||
"- Less important for short-dated options\n",
|
||
"- Higher rates benefit calls, hurt puts\n",
|
||
"- Often the least-monitored Greek"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "7540e4c7",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.630104Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.630035Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:14.631996Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:14.631683Z"
|
||
},
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.004696,
|
||
"end_time": "2026-06-13T02:33:14.632327+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.627631+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"def rho(S: float, K: float, T: float, r: float, sigma: float, option_type: str = \"call\") -> float:\n",
|
||
" \"\"\"\n",
|
||
" Compute Black-Scholes rho (per 1 point change in rate).\n",
|
||
" Divide by 100 for rho per 1% change.\n",
|
||
" \"\"\"\n",
|
||
" if T <= 0:\n",
|
||
" return 0.0\n",
|
||
"\n",
|
||
" d_2 = d2(S, K, T, r, sigma)\n",
|
||
"\n",
|
||
" if option_type.lower() == \"call\":\n",
|
||
" return K * T * np.exp(-r * T) * stats.norm.cdf(d_2)\n",
|
||
" else:\n",
|
||
" return -K * T * np.exp(-r * T) * stats.norm.cdf(-d_2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0c0291c4",
|
||
"metadata": {
|
||
"lines_to_next_cell": 2,
|
||
"papermill": {
|
||
"duration": 0.001866,
|
||
"end_time": "2026-06-13T02:33:14.636103+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.634237+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### All Greeks Summary Function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"id": "773422ff",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.640571Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:14.640500Z",
|
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"iopub.status.idle": "2026-06-13T02:33:14.643461Z",
|
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"shell.execute_reply": "2026-06-13T02:33:14.643110Z"
|
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},
|
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"papermill": {
|
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"duration": 0.005805,
|
||
"end_time": "2026-06-13T02:33:14.643797+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.637992+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"=== Greeks for ATM Call (S=K=100, T=0.25yr, σ=20%) ===\n",
|
||
" Delta: 0.569460\n",
|
||
" Gamma: 0.039288\n",
|
||
" Vega: 0.196440\n",
|
||
" Theta: -0.028696\n",
|
||
" Rho: 0.130828\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"def compute_all_greeks(\n",
|
||
" S: float, K: float, T: float, r: float, sigma: float, option_type: str = \"call\"\n",
|
||
") -> dict:\n",
|
||
" \"\"\"Compute all Greeks for an option.\"\"\"\n",
|
||
" return {\n",
|
||
" \"delta\": delta(S, K, T, r, sigma, option_type),\n",
|
||
" \"gamma\": gamma(S, K, T, r, sigma),\n",
|
||
" \"vega\": vega(S, K, T, r, sigma) / 100, # Per 1% vol change\n",
|
||
" \"theta\": theta(S, K, T, r, sigma, option_type) / 365, # Daily\n",
|
||
" \"rho\": rho(S, K, T, r, sigma, option_type) / 100, # Per 1% rate change\n",
|
||
" }\n",
|
||
"\n",
|
||
"\n",
|
||
"# Test the Greeks\n",
|
||
"test_greeks = compute_all_greeks(S=100, K=100, T=0.25, r=0.05, sigma=0.20)\n",
|
||
"\n",
|
||
"print(\"=== Greeks for ATM Call (S=K=100, T=0.25yr, σ=20%) ===\")\n",
|
||
"for greek, value in test_greeks.items():\n",
|
||
" print(f\"{greek.capitalize():>6}: {value:>10.6f}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "adaf3998",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.001924,
|
||
"end_time": "2026-06-13T02:33:14.647716+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.645792+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"## 4. Greeks Visualization\n",
|
||
"\n",
|
||
"Understanding how Greeks behave across different strikes and times to\n",
|
||
"expiration is crucial for option traders."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "be0c060e",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:14.652198Z",
|
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"iopub.status.busy": "2026-06-13T02:33:14.652131Z",
|
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|
||
"shell.execute_reply": "2026-06-13T02:33:14.671625Z"
|
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},
|
||
"papermill": {
|
||
"duration": 0.022554,
|
||
"end_time": "2026-06-13T02:33:14.672209+00:00",
|
||
"exception": false,
|
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"start_time": "2026-06-13T02:33:14.649655+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Generate data for visualization\n",
|
||
"strikes = np.linspace(80, 120, 41)\n",
|
||
"S_0 = 100\n",
|
||
"r_0 = 0.05\n",
|
||
"sigma_0 = 0.20\n",
|
||
"times = [0.25, 0.5, 1.0] # 3mo, 6mo, 1yr\n",
|
||
"\n",
|
||
"# Compute Greeks across strikes for different expirations\n",
|
||
"greeks_data = []\n",
|
||
"for T_val in times:\n",
|
||
" for K_val in strikes:\n",
|
||
" greeks = compute_all_greeks(S_0, K_val, T_val, r_0, sigma_0, \"call\")\n",
|
||
" greeks_data.append(\n",
|
||
" {\n",
|
||
" \"strike\": K_val,\n",
|
||
" \"moneyness\": S_0 / K_val,\n",
|
||
" \"time_to_exp\": f\"{int(T_val * 12)}M\",\n",
|
||
" \"T\": T_val,\n",
|
||
" **greeks,\n",
|
||
" }\n",
|
||
" )\n",
|
||
"\n",
|
||
"greeks_df = pl.DataFrame(greeks_data)"
|
||
]
|
||
},
|
||
{
|
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"cell_type": "markdown",
|
||
"id": "54a7e5f7",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.001924,
|
||
"end_time": "2026-06-13T02:33:14.676199+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:14.674275+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Delta vs Moneyness\n",
|
||
"\n",
|
||
"Delta transitions from 0 (deep OTM) to 1 (deep ITM), with the steepest\n",
|
||
"slope at ATM. Shorter-dated options have sharper transitions."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"id": "ee9537cf",
|
||
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|
||
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|
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"iopub.status.idle": "2026-06-13T02:33:15.545181Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.544781Z"
|
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},
|
||
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|
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|
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|
||
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|
||
"status": "completed"
|
||
}
|
||
},
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|
||
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|
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"linecolor": "white",
|
||
"ticks": ""
|
||
},
|
||
"bgcolor": "#E5ECF6",
|
||
"caxis": {
|
||
"gridcolor": "white",
|
||
"linecolor": "white",
|
||
"ticks": ""
|
||
}
|
||
},
|
||
"title": {
|
||
"x": 0.05
|
||
},
|
||
"xaxis": {
|
||
"automargin": true,
|
||
"gridcolor": "white",
|
||
"linecolor": "white",
|
||
"ticks": "",
|
||
"title": {
|
||
"standoff": 15
|
||
},
|
||
"zerolinecolor": "white",
|
||
"zerolinewidth": 2
|
||
},
|
||
"yaxis": {
|
||
"automargin": true,
|
||
"gridcolor": "white",
|
||
"linecolor": "white",
|
||
"ticks": "",
|
||
"title": {
|
||
"standoff": 15
|
||
},
|
||
"zerolinecolor": "white",
|
||
"zerolinewidth": 2
|
||
}
|
||
}
|
||
},
|
||
"title": {
|
||
"text": "Call Delta vs Strike Price"
|
||
},
|
||
"xaxis": {
|
||
"anchor": "y",
|
||
"domain": [
|
||
0.0,
|
||
1.0
|
||
],
|
||
"title": {
|
||
"text": "Strike Price ($)"
|
||
}
|
||
},
|
||
"yaxis": {
|
||
"anchor": "x",
|
||
"domain": [
|
||
0.0,
|
||
1.0
|
||
],
|
||
"title": {
|
||
"text": "Delta"
|
||
}
|
||
}
|
||
}
|
||
},
|
||
"image/png": 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"
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = px.line(\n",
|
||
" greeks_df.to_pandas(),\n",
|
||
" x=\"strike\",\n",
|
||
" y=\"delta\",\n",
|
||
" color=\"time_to_exp\",\n",
|
||
" title=\"Call Delta vs Strike Price\",\n",
|
||
" labels={\"strike\": \"Strike Price ($)\", \"delta\": \"Delta\", \"time_to_exp\": \"Expiration\"},\n",
|
||
")\n",
|
||
"fig.add_vline(x=100, line_dash=\"dash\", line_color=\"gray\", annotation_text=\"ATM\")\n",
|
||
"fig.update_layout(height=400)\n",
|
||
"fig.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8129bd3d",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.002773,
|
||
"end_time": "2026-06-13T02:33:15.551298+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.548525+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Gamma Concentration Near ATM\n",
|
||
"\n",
|
||
"Gamma peaks at ATM and increases dramatically as expiration approaches.\n",
|
||
"This is why short-dated ATM options are difficult to hedge."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"id": "3088fae1",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.557732Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.557629Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:15.612787Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.612324Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.059035,
|
||
"end_time": "2026-06-13T02:33:15.613171+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.554136+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"application/vnd.plotly.v1+json": {
|
||
"config": {
|
||
"plotlyServerURL": "https://plot.ly"
|
||
},
|
||
"data": [
|
||
{
|
||
"hovertemplate": "Expiration=3M<br>Strike Price ($)=%{x}<br>Gamma=%{y}<extra></extra>",
|
||
"legendgroup": "3M",
|
||
"line": {
|
||
"color": "#636efa",
|
||
"dash": "solid"
|
||
},
|
||
"marker": {
|
||
"symbol": "circle"
|
||
},
|
||
"mode": "lines",
|
||
"name": "3M",
|
||
"orientation": "v",
|
||
"showlegend": true,
|
||
"type": "scatter",
|
||
"x": {
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"
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = px.line(\n",
|
||
" greeks_df.to_pandas(),\n",
|
||
" x=\"strike\",\n",
|
||
" y=\"gamma\",\n",
|
||
" color=\"time_to_exp\",\n",
|
||
" title=\"Gamma vs Strike Price\",\n",
|
||
" labels={\"strike\": \"Strike Price ($)\", \"gamma\": \"Gamma\", \"time_to_exp\": \"Expiration\"},\n",
|
||
")\n",
|
||
"fig.add_vline(x=100, line_dash=\"dash\", line_color=\"gray\", annotation_text=\"ATM\")\n",
|
||
"fig.update_layout(height=400)\n",
|
||
"fig.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ff4de30e",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.00372,
|
||
"end_time": "2026-06-13T02:33:15.620733+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.617013+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Theta Decay Acceleration\n",
|
||
"\n",
|
||
"Theta (time decay) accelerates as expiration approaches. Options lose\n",
|
||
"value faster in their final weeks."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"id": "eeda3c27",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.628923Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.628751Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:15.687366Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.686952Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.063406,
|
||
"end_time": "2026-06-13T02:33:15.687719+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.624313+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"application/vnd.plotly.v1+json": {
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"
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = px.line(\n",
|
||
" greeks_df.to_pandas(),\n",
|
||
" x=\"strike\",\n",
|
||
" y=\"theta\",\n",
|
||
" color=\"time_to_exp\",\n",
|
||
" title=\"Daily Theta vs Strike Price\",\n",
|
||
" labels={\n",
|
||
" \"strike\": \"Strike Price ($)\",\n",
|
||
" \"theta\": \"Theta ($/day)\",\n",
|
||
" \"time_to_exp\": \"Expiration\",\n",
|
||
" },\n",
|
||
")\n",
|
||
"fig.add_vline(x=100, line_dash=\"dash\", line_color=\"gray\", annotation_text=\"ATM\")\n",
|
||
"fig.update_layout(height=400)\n",
|
||
"fig.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8ead9a3b",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.004459,
|
||
"end_time": "2026-06-13T02:33:15.696791+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.692332+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Vega Term Structure\n",
|
||
"\n",
|
||
"Longer-dated options have higher vega - they're more sensitive to\n",
|
||
"volatility changes. This makes sense: more time means more opportunity\n",
|
||
"for volatility to impact the final payoff."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"id": "b97fe7bd",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.706262Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.706163Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:15.751269Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.750677Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.050801,
|
||
"end_time": "2026-06-13T02:33:15.751888+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.701087+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"application/vnd.plotly.v1+json": {
|
||
"config": {
|
||
"plotlyServerURL": "https://plot.ly"
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||
},
|
||
"data": [
|
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{
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|
||
"legendgroup": "3M",
|
||
"line": {
|
||
"color": "#636efa",
|
||
"dash": "solid"
|
||
},
|
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"marker": {
|
||
"symbol": "circle"
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},
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||
"mode": "lines",
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||
"name": "3M",
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"orientation": "v",
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"showlegend": true,
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"type": "scatter",
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"x": {
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"dtype": "f8"
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},
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"xaxis": "x",
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"y": {
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"bdata": "Eqw8/H6Uhj8AoU/UrDaOP4WsFYDD1pM/Q894yR6WmT/P9h0MsTagP6JZoJdQNKQ/tkI3nPfEqD+FNWdu0uOtP2bcWrDNwrE/BkmRyzDMtD+suz3/2wG4P/FlHz+oVLs/6mIwJP+yvj9P1C5PxATBP4k7Lyn9ocI/akfLeP0mxD/UdEcnBYrFP5bYbmUvwsY/rAl899THxz/J3EMs3JTIP9oI9THyJMk/wwBHVqt1yT+kSmWqiYbJPxFmJE/rWMk/06vmNuPvyD9WxbFVAFDIP66lGPcHf8c/JoltQqiDxj8/kyHgJ2XFP9jmMEcXK8Q/9Dj7iwfdwj+46DOySYLBP24hnZi4IcA/NNtAVx2DvT8FHsBoj866PxpGssEcL7g/kudiHWmstT/htvrwaUyzPwpgHEh5E7E/cvqgUOkIrj9zgD4NyUGqPw==",
|
||
"dtype": "f8"
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},
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"yaxis": "y"
|
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},
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{
|
||
"hovertemplate": "Expiration=6M<br>Strike Price ($)=%{x}<br>Vega ($/1% vol)=%{y}<extra></extra>",
|
||
"legendgroup": "6M",
|
||
"line": {
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"color": "#EF553B",
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"dash": "solid"
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},
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"marker": {
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"symbol": "circle"
|
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},
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"mode": "lines",
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"name": "6M",
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"orientation": "v",
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"showlegend": true,
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"type": "scatter",
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"dtype": "f8"
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},
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"xaxis": "x",
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"y": {
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"bdata": "+5TEVp1Mqz86KSFbaeyvP+rFVi42fbI/TuETupk4tT8yRPpATCS4P09Y+lLmOrs/oX8hM711vj8TSoerf+bAPwwJX6/tm8I/JWIFDFhWxD8abCXfoRDGPz8sDC+Axcc/AywkjZlvyT9qlwMBpgnLP9Gc6huOjsw/O+V1KYj5zT8lvymSMkbPPyagbVZVONA/FzgStc+60D9PFh27LynRP+sIgE9xgtE/8xbbPefF0T/xKYk/O/PRP/wqOOFrCtI/YiLze8gL0j9CZWiE6/fRP0BoUnuzz9E/ppJXzjqU0T+f47X5zkbRP8HSAznn6NA/J0OwEBt80D94TjzzGALQP0lw6Hk6+c4/wX1ub9PazT8EYEude6zMP1R4gx+fccs/5N0jIIstyj+tY+N7Y+PIP1ajYEoalsc/9AAmQ2lIxj/27LXszPzEPw==",
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||
"dtype": "f8"
|
||
},
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||
"yaxis": "y"
|
||
},
|
||
{
|
||
"hovertemplate": "Expiration=12M<br>Strike Price ($)=%{x}<br>Vega ($/1% vol)=%{y}<extra></extra>",
|
||
"legendgroup": "12M",
|
||
"line": {
|
||
"color": "#00cc96",
|
||
"dash": "solid"
|
||
},
|
||
"marker": {
|
||
"symbol": "circle"
|
||
},
|
||
"mode": "lines",
|
||
"name": "12M",
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||
"orientation": "v",
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||
"showlegend": true,
|
||
"type": "scatter",
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"x": {
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"bdata": "AAAAAAAAVEAAAAAAAEBUQAAAAAAAgFRAAAAAAADAVEAAAAAAAABVQAAAAAAAQFVAAAAAAACAVUAAAAAAAMBVQAAAAAAAAFZAAAAAAABAVkAAAAAAAIBWQAAAAAAAwFZAAAAAAAAAV0AAAAAAAEBXQAAAAAAAgFdAAAAAAADAV0AAAAAAAABYQAAAAAAAQFhAAAAAAACAWEAAAAAAAMBYQAAAAAAAAFlAAAAAAABAWUAAAAAAAIBZQAAAAAAAwFlAAAAAAAAAWkAAAAAAAEBaQAAAAAAAgFpAAAAAAADAWkAAAAAAAABbQAAAAAAAQFtAAAAAAACAW0AAAAAAAMBbQAAAAAAAAFxAAAAAAABAXEAAAAAAAIBcQAAAAAAAwFxAAAAAAAAAXUAAAAAAAEBdQAAAAAAAgF1AAAAAAADAXUAAAAAAAABeQA==",
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"dtype": "f8"
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},
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"xaxis": "x",
|
||
"y": {
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"
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"fig = px.line(\n",
|
||
" greeks_df.to_pandas(),\n",
|
||
" x=\"strike\",\n",
|
||
" y=\"vega\",\n",
|
||
" color=\"time_to_exp\",\n",
|
||
" title=\"Vega vs Strike Price\",\n",
|
||
" labels={\n",
|
||
" \"strike\": \"Strike Price ($)\",\n",
|
||
" \"vega\": \"Vega ($/1% vol)\",\n",
|
||
" \"time_to_exp\": \"Expiration\",\n",
|
||
" },\n",
|
||
")\n",
|
||
"fig.add_vline(x=100, line_dash=\"dash\", line_color=\"gray\", annotation_text=\"ATM\")\n",
|
||
"fig.update_layout(height=400)\n",
|
||
"fig.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cf79f607",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.005398,
|
||
"end_time": "2026-06-13T02:33:15.763701+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.758303+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"## 5. Validation Against AlgoSeek Data\n",
|
||
"\n",
|
||
"Now we validate our Greeks computations against the pre-computed values\n",
|
||
"in the AlgoSeek options dataset. We'll use a risk-free rate from FRED."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"id": "005c8ea3",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.774768Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.774672Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:15.831080Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.830739Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.062697,
|
||
"end_time": "2026-06-13T02:33:15.831482+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.768785+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Loaded 598,046 option records\n",
|
||
"Columns: ['symbol', 'call_put', 'option_style', 'strike', 'expiration', 'years_to_maturity', 'days_to_maturity', 'underlying_price', 'bid', 'ask', 'mid_price', 'implied_vol', 'theo_price', 'delta', 'gamma', 'theta', 'vega', 'rho', 'iv_convergence', 'year', 'timestamp']\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"options = load_sp500_options_eda(\n",
|
||
" symbols=[\"AAPL\"],\n",
|
||
" start_date=\"2020-01-01\",\n",
|
||
" end_date=\"2020-12-31\",\n",
|
||
")\n",
|
||
"\n",
|
||
"print(f\"Loaded {len(options):,} option records\")\n",
|
||
"print(f\"Columns: {options.columns}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"id": "bdfeae53",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.842567Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.842481Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:15.851352Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.851052Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.014789,
|
||
"end_time": "2026-06-13T02:33:15.851683+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.836894+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Filtered to 185,450 options\n"
|
||
]
|
||
},
|
||
{
|
||
"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, 21)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>symbol</th><th>call_put</th><th>option_style</th><th>strike</th><th>expiration</th><th>years_to_maturity</th><th>days_to_maturity</th><th>underlying_price</th><th>bid</th><th>ask</th><th>mid_price</th><th>implied_vol</th><th>theo_price</th><th>delta</th><th>gamma</th><th>theta</th><th>vega</th><th>rho</th><th>iv_convergence</th><th>year</th><th>timestamp</th></tr><tr><td>str</td><td>str</td><td>str</td><td>f64</td><td>date</td><td>f64</td><td>i32</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>str</td><td>i64</td><td>date</td></tr></thead><tbody><tr><td>"AAPL"</td><td>"C"</td><td>"A"</td><td>185.0</td><td>2020-01-24</td><td>0.0601093</td><td>22</td><td>300.59</td><td>113.6</td><td>117.5</td><td>115.55</td><td>0.39649</td><td>115.77483</td><td>1.0</td><td>0.0</td><td>-0.00839</td><td>0.00003</td><td>0.11109</td><td>"IntrVal_FlatExtrapol"</td><td>2020</td><td>2020-01-02</td></tr><tr><td>"AAPL"</td><td>"C"</td><td>"A"</td><td>190.0</td><td>2020-01-24</td><td>0.0601093</td><td>22</td><td>300.59</td><td>108.65</td><td>112.5</td><td>110.575</td><td>0.39649</td><td>110.77984</td><td>1.0</td><td>0.0</td><td>-0.00862</td><td>0.00003</td><td>0.11409</td><td>"IntrVal_FlatExtrapol"</td><td>2020</td><td>2020-01-02</td></tr><tr><td>"AAPL"</td><td>"C"</td><td>"A"</td><td>195.0</td><td>2020-01-24</td><td>0.0601093</td><td>22</td><td>300.59</td><td>103.65</td><td>107.5</td><td>105.575</td><td>0.39649</td><td>105.78485</td><td>1.0</td><td>0.0</td><td>-0.00886</td><td>0.00003</td><td>0.1171</td><td>"IntrVal_FlatExtrapol"</td><td>2020</td><td>2020-01-02</td></tr><tr><td>"AAPL"</td><td>"C"</td><td>"A"</td><td>200.0</td><td>2020-01-24</td><td>0.0601093</td><td>22</td><td>300.59</td><td>98.65</td><td>102.5</td><td>100.575</td><td>0.65569</td><td>100.86079</td><td>0.99558</td><td>0.00027</td><td>-0.02242</td><td>0.0096</td><td>0.11925</td><td>"IntrVal_PutCallPair"</td><td>2020</td><td>2020-01-02</td></tr><tr><td>"AAPL"</td><td>"C"</td><td>"A"</td><td>205.0</td><td>2020-01-24</td><td>0.0601093</td><td>22</td><td>300.59</td><td>93.7</td><td>97.5</td><td>95.6</td><td>0.60891</td><td>95.8556</td><td>0.99588</td><td>0.00027</td><td>-0.02092</td><td>0.00902</td><td>0.12231</td><td>"IntrVal_PutCallPair"</td><td>2020</td><td>2020-01-02</td></tr></tbody></table></div>"
|
||
],
|
||
"text/plain": [
|
||
"shape: (5, 21)\n",
|
||
"┌────────┬──────────┬──────────────┬────────┬───┬─────────┬────────────────────┬──────┬────────────┐\n",
|
||
"│ symbol ┆ call_put ┆ option_style ┆ strike ┆ … ┆ rho ┆ iv_convergence ┆ year ┆ timestamp │\n",
|
||
"│ --- ┆ --- ┆ --- ┆ --- ┆ ┆ --- ┆ --- ┆ --- ┆ --- │\n",
|
||
"│ str ┆ str ┆ str ┆ f64 ┆ ┆ f64 ┆ str ┆ i64 ┆ date │\n",
|
||
"╞════════╪══════════╪══════════════╪════════╪═══╪═════════╪════════════════════╪══════╪════════════╡\n",
|
||
"│ AAPL ┆ C ┆ A ┆ 185.0 ┆ … ┆ 0.11109 ┆ IntrVal_FlatExtrap ┆ 2020 ┆ 2020-01-02 │\n",
|
||
"│ ┆ ┆ ┆ ┆ ┆ ┆ ol ┆ ┆ │\n",
|
||
"│ AAPL ┆ C ┆ A ┆ 190.0 ┆ … ┆ 0.11409 ┆ IntrVal_FlatExtrap ┆ 2020 ┆ 2020-01-02 │\n",
|
||
"│ ┆ ┆ ┆ ┆ ┆ ┆ ol ┆ ┆ │\n",
|
||
"│ AAPL ┆ C ┆ A ┆ 195.0 ┆ … ┆ 0.1171 ┆ IntrVal_FlatExtrap ┆ 2020 ┆ 2020-01-02 │\n",
|
||
"│ ┆ ┆ ┆ ┆ ┆ ┆ ol ┆ ┆ │\n",
|
||
"│ AAPL ┆ C ┆ A ┆ 200.0 ┆ … ┆ 0.11925 ┆ IntrVal_PutCallPai ┆ 2020 ┆ 2020-01-02 │\n",
|
||
"│ ┆ ┆ ┆ ┆ ┆ ┆ r ┆ ┆ │\n",
|
||
"│ AAPL ┆ C ┆ A ┆ 205.0 ┆ … ┆ 0.12231 ┆ IntrVal_PutCallPai ┆ 2020 ┆ 2020-01-02 │\n",
|
||
"│ ┆ ┆ ┆ ┆ ┆ ┆ r ┆ ┆ │\n",
|
||
"└────────┴──────────┴──────────────┴────────┴───┴─────────┴────────────────────┴──────┴────────────┘"
|
||
]
|
||
},
|
||
"execution_count": 22,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Filter to liquid options for validation\n",
|
||
"# ATM options with reasonable time to expiration\n",
|
||
"options_filtered = options.filter(\n",
|
||
" (pl.col(\"days_to_maturity\").is_between(20, 90))\n",
|
||
" & (pl.col(\"implied_vol\").is_not_null())\n",
|
||
" & (pl.col(\"implied_vol\") > 0.05)\n",
|
||
" & (pl.col(\"implied_vol\") < 2.0)\n",
|
||
" & (pl.col(\"delta\").is_not_null())\n",
|
||
")\n",
|
||
"\n",
|
||
"print(f\"Filtered to {len(options_filtered):,} options\")\n",
|
||
"options_filtered.head(5)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"id": "16eacef5",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.863001Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.862913Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:15.928784Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.928316Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.072061,
|
||
"end_time": "2026-06-13T02:33:15.929224+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.857163+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Compute our Greeks for each option\n",
|
||
"validation_results = []\n",
|
||
"\n",
|
||
"for row in options_filtered.head(N_GREEKS_VALIDATE).iter_rows(named=True):\n",
|
||
" S = row[\"underlying_price\"]\n",
|
||
" K = row[\"strike\"]\n",
|
||
" T = row[\"years_to_maturity\"]\n",
|
||
" sigma = row[\"implied_vol\"]\n",
|
||
" opt_type = \"call\" if row[\"call_put\"] == \"C\" else \"put\"\n",
|
||
"\n",
|
||
" # Our computed values\n",
|
||
" our_delta = delta(S, K, T, RISK_FREE_RATE, sigma, opt_type)\n",
|
||
" our_gamma = gamma(S, K, T, RISK_FREE_RATE, sigma)\n",
|
||
" our_vega = vega(S, K, T, RISK_FREE_RATE, sigma) / 100\n",
|
||
" our_theta = theta(S, K, T, RISK_FREE_RATE, sigma, opt_type) / 365\n",
|
||
"\n",
|
||
" # AlgoSeek values\n",
|
||
" algoseek_delta = row[\"delta\"]\n",
|
||
" algoseek_gamma = row[\"gamma\"]\n",
|
||
" algoseek_vega = row[\"vega\"]\n",
|
||
" algoseek_theta = row[\"theta\"]\n",
|
||
"\n",
|
||
" validation_results.append(\n",
|
||
" {\n",
|
||
" \"symbol\": row[\"symbol\"],\n",
|
||
" \"strike\": K,\n",
|
||
" \"days_to_exp\": row[\"days_to_maturity\"],\n",
|
||
" \"option_type\": opt_type,\n",
|
||
" \"iv\": sigma,\n",
|
||
" \"our_delta\": our_delta,\n",
|
||
" \"algoseek_delta\": algoseek_delta,\n",
|
||
" \"our_gamma\": our_gamma,\n",
|
||
" \"algoseek_gamma\": algoseek_gamma,\n",
|
||
" \"our_vega\": our_vega,\n",
|
||
" \"algoseek_vega\": algoseek_vega,\n",
|
||
" \"our_theta\": our_theta,\n",
|
||
" \"algoseek_theta\": algoseek_theta,\n",
|
||
" }\n",
|
||
" )\n",
|
||
"\n",
|
||
"validation_df = pl.DataFrame(validation_results)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"id": "5c70cd54",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.961457Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.961282Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:15.966328Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:15.965764Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.027288,
|
||
"end_time": "2026-06-13T02:33:15.966754+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.939466+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"=== Greeks Validation Summary ===\n",
|
||
"Options validated: 500\n",
|
||
"\n",
|
||
"Delta:\n",
|
||
" Mean error: 0.002226\n",
|
||
" Median error: 0.000782\n",
|
||
" Max error: 0.010556\n",
|
||
"\n",
|
||
"Gamma:\n",
|
||
" Mean error: 0.000068\n",
|
||
" Median error: 0.000030\n",
|
||
" Max error: 0.000877\n",
|
||
"\n",
|
||
"Vega:\n",
|
||
" Mean error: 0.002328\n",
|
||
" Median error: 0.001139\n",
|
||
" Max error: 0.021729\n",
|
||
"\n",
|
||
"Theta:\n",
|
||
" Mean error: 0.001260\n",
|
||
" Median error: 0.000943\n",
|
||
" Max error: 0.004631\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Calculate validation errors\n",
|
||
"validation_df = validation_df.with_columns(\n",
|
||
" delta_error=(pl.col(\"our_delta\") - pl.col(\"algoseek_delta\")).abs(),\n",
|
||
" gamma_error=(pl.col(\"our_gamma\") - pl.col(\"algoseek_gamma\")).abs(),\n",
|
||
" vega_error=(pl.col(\"our_vega\") - pl.col(\"algoseek_vega\")).abs(),\n",
|
||
" theta_error=(pl.col(\"our_theta\") - pl.col(\"algoseek_theta\")).abs(),\n",
|
||
")\n",
|
||
"\n",
|
||
"# Summary statistics\n",
|
||
"print(\"=== Greeks Validation Summary ===\")\n",
|
||
"print(f\"Options validated: {len(validation_df)}\")\n",
|
||
"print()\n",
|
||
"\n",
|
||
"for greek in [\"delta\", \"gamma\", \"vega\", \"theta\"]:\n",
|
||
" error_col = f\"{greek}_error\"\n",
|
||
" stats_row = validation_df.select(\n",
|
||
" pl.col(error_col).mean().alias(\"mean\"),\n",
|
||
" pl.col(error_col).median().alias(\"median\"),\n",
|
||
" pl.col(error_col).max().alias(\"max\"),\n",
|
||
" )\n",
|
||
" print(f\"{greek.capitalize()}:\")\n",
|
||
" print(f\" Mean error: {stats_row['mean'][0]:.6f}\")\n",
|
||
" print(f\" Median error: {stats_row['median'][0]:.6f}\")\n",
|
||
" print(f\" Max error: {stats_row['max'][0]:.6f}\")\n",
|
||
" print()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "642fc634",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.005292,
|
||
"end_time": "2026-06-13T02:33:15.981600+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.976308+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Validation Scatter Plots"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"id": "1883b587",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:15.993103Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:15.992993Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:16.164173Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:16.163505Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.177831,
|
||
"end_time": "2026-06-13T02:33:16.164619+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:15.986788+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"application/vnd.plotly.v1+json": {
|
||
"config": {
|
||
"plotlyServerURL": "https://plot.ly"
|
||
},
|
||
"data": [
|
||
{
|
||
"marker": {
|
||
"opacity": 0.5,
|
||
"size": 4
|
||
},
|
||
"mode": "markers",
|
||
"name": "Delta",
|
||
"type": "scatter",
|
||
"x": [
|
||
1.0,
|
||
1.0,
|
||
1.0,
|
||
0.99558,
|
||
0.99588,
|
||
0.99397,
|
||
0.99305,
|
||
0.99177,
|
||
0.98895,
|
||
0.98803,
|
||
0.98596,
|
||
0.98437,
|
||
0.98299,
|
||
0.98069,
|
||
0.98056,
|
||
0.98104,
|
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"
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Build all four panels in a single cell — splitting figure construction across\n",
|
||
"# cells lets papermill flush the inline backend mid-render and capture the\n",
|
||
"# Delta+Gamma intermediate, leaving Vega/Theta empty in the published figure.\n",
|
||
"fig = make_subplots(rows=2, cols=2, subplot_titles=[\"Delta\", \"Gamma\", \"Vega\", \"Theta\"])\n",
|
||
"\n",
|
||
"\n",
|
||
"# Helper: draw scatter + reference 45° line into one panel.\n",
|
||
"def _add_validation_panel(row: int, col: int, x_col: str, y_col: str, name: str) -> None:\n",
|
||
" x_vals = validation_df[x_col].to_list()\n",
|
||
" y_vals = validation_df[y_col].to_list()\n",
|
||
" fig.add_trace(\n",
|
||
" go.Scatter(\n",
|
||
" x=x_vals,\n",
|
||
" y=y_vals,\n",
|
||
" mode=\"markers\",\n",
|
||
" marker=dict(size=4, opacity=0.5),\n",
|
||
" name=name,\n",
|
||
" ),\n",
|
||
" row=row,\n",
|
||
" col=col,\n",
|
||
" )\n",
|
||
" lo = min(min(x_vals), min(y_vals))\n",
|
||
" hi = max(max(x_vals), max(y_vals))\n",
|
||
" fig.add_trace(\n",
|
||
" go.Scatter(\n",
|
||
" x=[lo, hi],\n",
|
||
" y=[lo, hi],\n",
|
||
" mode=\"lines\",\n",
|
||
" line=dict(dash=\"dash\", color=\"red\"),\n",
|
||
" showlegend=False,\n",
|
||
" ),\n",
|
||
" row=row,\n",
|
||
" col=col,\n",
|
||
" )\n",
|
||
"\n",
|
||
"\n",
|
||
"_add_validation_panel(1, 1, \"algoseek_delta\", \"our_delta\", \"Delta\")\n",
|
||
"_add_validation_panel(1, 2, \"algoseek_gamma\", \"our_gamma\", \"Gamma\")\n",
|
||
"_add_validation_panel(2, 1, \"algoseek_vega\", \"our_vega\", \"Vega\")\n",
|
||
"_add_validation_panel(2, 2, \"algoseek_theta\", \"our_theta\", \"Theta\")\n",
|
||
"\n",
|
||
"fig.update_layout(\n",
|
||
" height=600,\n",
|
||
" title_text=\"Our Greeks vs AlgoSeek (perfect = diagonal line)\",\n",
|
||
" showlegend=False,\n",
|
||
")\n",
|
||
"fig.update_xaxes(title_text=\"AlgoSeek\", row=2, col=1)\n",
|
||
"fig.update_xaxes(title_text=\"AlgoSeek\", row=2, col=2)\n",
|
||
"fig.update_yaxes(title_text=\"Our Calculation\", row=1, col=1)\n",
|
||
"fig.update_yaxes(title_text=\"Our Calculation\", row=2, col=1)\n",
|
||
"\n",
|
||
"fig.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "799587b8",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.007439,
|
||
"end_time": "2026-06-13T02:33:16.179652+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:16.172213+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"### Sources of Discrepancy\n",
|
||
"\n",
|
||
"Small differences between our calculations and AlgoSeek's pre-computed values\n",
|
||
"can arise from:\n",
|
||
"\n",
|
||
"1. **Risk-free rate**: We used a constant rate; they may use term-matched rates\n",
|
||
"2. **Dividend handling**: We ignored dividends; they may adjust for them\n",
|
||
"3. **American vs European**: Our formulas assume European exercise\n",
|
||
"4. **Numerical precision**: Different root-finding algorithms\n",
|
||
"5. **Timestamp differences**: Greeks change throughout the day"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "34831fe6",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.007341,
|
||
"end_time": "2026-06-13T02:33:16.194333+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:16.186992+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"## 6. Computing IV from Market Prices\n",
|
||
"\n",
|
||
"Let's demonstrate computing implied volatility from the observed option\n",
|
||
"prices and compare to the provided IV values."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"id": "bb6c7cc5",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2026-06-13T02:33:16.209798Z",
|
||
"iopub.status.busy": "2026-06-13T02:33:16.209648Z",
|
||
"iopub.status.idle": "2026-06-13T02:33:16.339326Z",
|
||
"shell.execute_reply": "2026-06-13T02:33:16.338795Z"
|
||
},
|
||
"papermill": {
|
||
"duration": 0.138431,
|
||
"end_time": "2026-06-13T02:33:16.340022+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:16.201591+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Compute IV for a sample of options\n",
|
||
"iv_validation = []\n",
|
||
"\n",
|
||
"for row in options_filtered.head(N_IV_VALIDATE).iter_rows(named=True):\n",
|
||
" S = row[\"underlying_price\"]\n",
|
||
" K = row[\"strike\"]\n",
|
||
" T = row[\"years_to_maturity\"]\n",
|
||
" market_price = row[\"mid_price\"]\n",
|
||
" opt_type = \"call\" if row[\"call_put\"] == \"C\" else \"put\"\n",
|
||
"\n",
|
||
" if market_price is not None and market_price > 0:\n",
|
||
" computed_iv = implied_volatility(market_price, S, K, T, RISK_FREE_RATE, opt_type)\n",
|
||
"\n",
|
||
" if computed_iv is not None:\n",
|
||
" iv_validation.append(\n",
|
||
" {\n",
|
||
" \"symbol\": row[\"symbol\"],\n",
|
||
" \"strike\": K,\n",
|
||
" \"days_to_exp\": row[\"days_to_maturity\"],\n",
|
||
" \"option_type\": opt_type,\n",
|
||
" \"market_price\": market_price,\n",
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" \"computed_iv\": computed_iv,\n",
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" \"algoseek_iv\": row[\"implied_vol\"],\n",
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" }\n",
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" )\n",
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"\n",
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"iv_df = pl.DataFrame(iv_validation)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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},
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{
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"name": "stdout",
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"text": [
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"=== IV Validation Summary ===\n",
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"Options validated: 179\n",
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"Mean IV difference: 0.0237\n",
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"Median IV difference: 0.0005\n",
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"Mean % difference: 7.26%\n"
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]
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}
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],
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" iv_diff=(pl.col(\"computed_iv\") - pl.col(\"algoseek_iv\")).abs(),\n",
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" iv_pct_diff=((pl.col(\"computed_iv\") - pl.col(\"algoseek_iv\")).abs() / pl.col(\"algoseek_iv\"))\n",
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" * 100,\n",
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")\n",
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"\n",
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"print(\"=== IV Validation Summary ===\")\n",
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"print(f\"Options validated: {len(iv_df)}\")\n",
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"print(f\"Mean IV difference: {iv_df['iv_diff'].mean():.4f}\")\n",
|
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"print(f\"Median IV difference: {iv_df['iv_diff'].median():.4f}\")\n",
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"print(f\"Mean % difference: {iv_df['iv_pct_diff'].mean():.2f}%\")"
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]
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},
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{
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"
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Scatter plot\n",
|
||
"fig = px.scatter(\n",
|
||
" iv_df.to_pandas(),\n",
|
||
" x=\"algoseek_iv\",\n",
|
||
" y=\"computed_iv\",\n",
|
||
" color=\"option_type\",\n",
|
||
" title=\"Computed IV vs AlgoSeek IV\",\n",
|
||
" labels={\n",
|
||
" \"algoseek_iv\": \"AlgoSeek IV\",\n",
|
||
" \"computed_iv\": \"Our Computed IV\",\n",
|
||
" \"option_type\": \"Type\",\n",
|
||
" },\n",
|
||
" opacity=0.6,\n",
|
||
")\n",
|
||
"fig.add_trace(\n",
|
||
" go.Scatter(\n",
|
||
" x=[0, 1],\n",
|
||
" y=[0, 1],\n",
|
||
" mode=\"lines\",\n",
|
||
" line=dict(dash=\"dash\", color=\"gray\"),\n",
|
||
" name=\"Perfect Match\",\n",
|
||
" )\n",
|
||
")\n",
|
||
"fig.update_layout(height=500)\n",
|
||
"fig.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "db3dc6b4",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.011308,
|
||
"end_time": "2026-06-13T02:33:16.451912+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:16.440604+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"## 7. Practical Considerations\n",
|
||
"\n",
|
||
"### When Black-Scholes Breaks Down\n",
|
||
"\n",
|
||
"| Scenario | Problem | Alternative Approach |\n",
|
||
"|----------|---------|---------------------|\n",
|
||
"| Deep OTM options | Log-normal underprices tails | Use jump-diffusion or local vol |\n",
|
||
"| Short-dated ATM | Gamma explosion | Use realized vol, not IV |\n",
|
||
"| Dividend stocks | Wrong forward price | Use dividend-adjusted models |\n",
|
||
"| American options | Early exercise value | Use binomial tree or approximations |\n",
|
||
"| Vol clustering | Constant vol assumption | Use GARCH or stochastic vol |\n",
|
||
"\n",
|
||
"### The Greeks in Practice\n",
|
||
"\n",
|
||
"**For Hedging:**\n",
|
||
"- Delta-hedge by trading underlying shares\n",
|
||
"- Gamma tells you how often to rebalance\n",
|
||
"- Vega exposure from vol moves often dominates\n",
|
||
"\n",
|
||
"**For Trading:**\n",
|
||
"- Greeks help identify relative value\n",
|
||
"- High gamma + low premium = potential mispricing\n",
|
||
"- Theta/vega ratio useful for vol trades\n",
|
||
"\n",
|
||
"**For Risk Management:**\n",
|
||
"- Aggregate portfolio Greeks\n",
|
||
"- Stress test under extreme scenarios\n",
|
||
"- Greeks are local approximations - large moves need full repricing"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b28143f8",
|
||
"metadata": {
|
||
"papermill": {
|
||
"duration": 0.00915,
|
||
"end_time": "2026-06-13T02:33:16.469898+00:00",
|
||
"exception": false,
|
||
"start_time": "2026-06-13T02:33:16.460748+00:00",
|
||
"status": "completed"
|
||
}
|
||
},
|
||
"source": [
|
||
"## 8. Key Takeaways\n",
|
||
"\n",
|
||
"1. Black-Scholes pricing recovers put-call parity to numerical precision\n",
|
||
" (~7e-15 on the test parameters); the same code base solves IV via Brent's\n",
|
||
" method to ~10⁻¹¹ accuracy on a closed-loop test.\n",
|
||
"2. Greeks computed in-house track the AlgoSeek vendor values closely on\n",
|
||
" AAPL options (20–90 DTE, IV ∈ [0.05, 2]): mean absolute errors are\n",
|
||
" ~2×10⁻³ for delta and vega, ~7×10⁻⁵ for gamma, ~1×10⁻³ for daily theta.\n",
|
||
"3. The remaining residual reflects modeling choices that the vendor handles\n",
|
||
" differently — term-matched risk-free rates, dividend treatment, American\n",
|
||
" early-exercise premium, and intraday timestamp drift in the inputs.\n",
|
||
"4. Cross-sectional IV recovery (≈180 options) yields a median absolute IV\n",
|
||
" diff of ~5×10⁻⁴ and a mean of ~0.024, with the residual concentrated in\n",
|
||
" deep OTM contracts where the loss surface is shallow.\n",
|
||
"5. Greeks are local sensitivities — the visualizations show how Δ steepens\n",
|
||
" and Γ peaks near ATM as expiration approaches, which is also the regime\n",
|
||
" where the Black-Scholes assumption set is most stressed.\n",
|
||
"\n",
|
||
"## Next Steps\n",
|
||
"\n",
|
||
"- Chapter 8: Build features from options data (IV signals, skew measures).\n",
|
||
"- Chapter 9: Evaluate IV-based signals for equity prediction.\n",
|
||
"- Chapter 12+: ML models using options-derived features.\n",
|
||
"- Chapter 16: Strategy backtests including the `sp500_options` short-straddle\n",
|
||
" case study and the `sp500_equity_option_analytics` IV-features case study."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"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": {
|
||
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