chore: import upstream snapshot with attribution
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wehub-resource-sync
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/*
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* QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals.
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* Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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using System;
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using System.Runtime.CompilerServices;
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using MathNet.Numerics.Distributions;
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using QuantConnect.Util;
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namespace QuantConnect.Indicators
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{
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/// <summary>
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/// Helper class for option greeks related indicators
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/// </summary>
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public class OptionGreekIndicatorsHelper
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{
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/// <summary>
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/// Number of steps in binomial tree simulation to obtain Greeks/IV
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/// </summary>
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public const int Steps = 200;
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/// <summary>
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/// Returns the Black theoretical price for the given arguments
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/// </summary>
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public static double BlackTheoreticalPrice(double volatility, double spotPrice, double strikePrice, double timeToExpiration, double riskFreeRate, double dividendYield, OptionRight optionType)
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{
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var d1 = CalculateD1(spotPrice, strikePrice, timeToExpiration, riskFreeRate, dividendYield, volatility);
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var d2 = CalculateD2(d1, volatility, timeToExpiration);
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var norm = new Normal();
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var optionPrice = 0.0;
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if (optionType == OptionRight.Call)
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{
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optionPrice = spotPrice * Math.Exp(-dividendYield * timeToExpiration) * norm.CumulativeDistribution(d1)
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- strikePrice * Math.Exp(-riskFreeRate * timeToExpiration) * norm.CumulativeDistribution(d2);
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}
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else if (optionType == OptionRight.Put)
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{
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optionPrice = strikePrice * Math.Exp(-riskFreeRate * timeToExpiration) * norm.CumulativeDistribution(-d2)
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- spotPrice * Math.Exp(-dividendYield * timeToExpiration) * norm.CumulativeDistribution(-d1);
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}
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else
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{
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throw new ArgumentException("Invalid option right.");
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}
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return optionPrice;
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}
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internal static double CalculateD1(double spotPrice, double strikePrice, double timeToExpiration, double riskFreeRate, double dividendYield, double volatility)
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{
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var numerator = Math.Log(spotPrice / strikePrice) + (riskFreeRate - dividendYield + 0.5 * volatility * volatility) * timeToExpiration;
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var denominator = volatility * Math.Sqrt(Math.Max(0, timeToExpiration));
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if (denominator == 0)
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{
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// return a random variable large enough to produce normal probability density close to 1
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return 10;
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}
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return numerator / denominator;
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}
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internal static double CalculateD2(double d1, double volatility, double timeToExpiration)
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{
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return d1 - volatility * Math.Sqrt(Math.Max(0, timeToExpiration));
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}
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/// <summary>
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/// Creates a Binomial Theoretical Price Tree from the given parameters
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/// </summary>
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/// <remarks>Reference: https://en.wikipedia.org/wiki/Binomial_options_pricing_model#Step_1:_Create_the_binomial_price_tree</remarks>
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public static double CRRTheoreticalPrice(double volatility, double spotPrice, double strikePrice,
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double timeToExpiration, double riskFreeRate, double dividendYield, OptionRight optionType, int steps = Steps)
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{
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var deltaTime = timeToExpiration / steps;
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var upFactor = Math.Exp(volatility * Math.Sqrt(deltaTime));
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if (upFactor == 1)
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{
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// Introduce a very small factor to avoid constant tree while staying low volatility
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upFactor = 1.0001;
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}
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var downFactor = 1 / upFactor;
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var probUp = (Math.Exp((riskFreeRate - dividendYield) * deltaTime) - downFactor) / (upFactor - downFactor);
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return BinomialTheoreticalPrice(deltaTime, probUp, upFactor, riskFreeRate, spotPrice, strikePrice, optionType, steps);
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}
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/// <summary>
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/// Creates the Forward Binomial Theoretical Price Tree from the given parameters
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/// </summary>
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public static double ForwardTreeTheoreticalPrice(double volatility, double spotPrice, double strikePrice,
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double timeToExpiration, double riskFreeRate, double dividendYield, OptionRight optionType, int steps = Steps)
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{
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var deltaTime = timeToExpiration / steps;
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var discount = Math.Exp((riskFreeRate - dividendYield) * deltaTime);
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var volatilityTimeSqrtDeltaTime = volatility * Math.Sqrt(deltaTime);
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var upFactor = Math.Exp(volatilityTimeSqrtDeltaTime) * discount;
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var downFactor = Math.Exp(-volatilityTimeSqrtDeltaTime) * discount;
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if (upFactor - downFactor == 0)
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{
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// Introduce a very small factor
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// to avoid constant tree while staying low volatility
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upFactor = 1.0001;
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downFactor = 0.9999;
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}
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var probUp = (discount - downFactor) / (upFactor - downFactor);
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return BinomialTheoreticalPrice(deltaTime, probUp, upFactor, riskFreeRate, spotPrice, strikePrice, optionType, steps);
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}
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private static double BinomialTheoreticalPrice(double deltaTime, double probUp, double upFactor, double riskFreeRate,
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double spotPrice, double strikePrice, OptionRight optionType, int steps = Steps)
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{
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var probDown = 1 - probUp;
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var values = new double[steps + 1];
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// Cache for exercise values for Call options to avoid recalculating them
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var exerciseValues = optionType == OptionRight.Call ? new double[2 * steps] : null;
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for (int i = 0; i < (exerciseValues?.Length ?? values.Length); i++)
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{
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if (i < values.Length)
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{
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var nextPrice = spotPrice * Math.Pow(upFactor, 2 * i - steps);
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values[i] = OptionPayoff.GetIntrinsicValue(nextPrice, strikePrice, optionType);
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}
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if (optionType == OptionRight.Call)
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{
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var nextPrice = spotPrice * Math.Pow(upFactor, i - steps);
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exerciseValues[i] = OptionPayoff.GetIntrinsicValue(nextPrice, strikePrice, optionType);
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}
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}
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var factor = Math.Exp(-riskFreeRate * deltaTime);
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var factorA = factor * probDown;
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var factorB = factor * probUp;
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for (var period = steps - 1; period >= 0; period--)
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{
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for (var i = 0; i <= period; i++)
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{
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var binomialValue = values[i] * factorA + values[i + 1] * factorB;
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// No advantage for American put option to exercise early in risk-neutral setting
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if (optionType == OptionRight.Put)
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{
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values[i] = binomialValue;
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continue;
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}
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values[i] = Math.Max(binomialValue, exerciseValues[2 * i - period + steps]);
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}
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}
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return values[0];
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public static double TimeTillExpiry(DateTime expiry, DateTime referenceDate)
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{
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return (expiry - referenceDate).TotalDays / 365d;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static double Divide(double numerator, double denominator)
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{
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if (denominator != 0)
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{
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return numerator / denominator;
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}
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//Log.Error("OptionGreekIndicatorsHelper.Divide(): Division by zero detected. Returning 0.");
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return 0;
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}
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}
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}
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