wehub-resource-sync
256 lines
14 KiB
C#
256 lines
14 KiB
C#
/*
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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 MathNet.Numerics.Distributions;
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using Python.Runtime;
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using QuantConnect.Data;
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namespace QuantConnect.Indicators
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{
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/// <summary>
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/// Option Theta indicator that calculate the theta of an option
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/// </summary>
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/// <remarks>sensitivity of option price on time decay</remarks>
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public class Theta : OptionGreeksIndicatorBase
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{
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="name">The name of this indicator</param>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYieldModel">Dividend yield model</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(string name, Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, IDividendYieldModel dividendYieldModel, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRateModel, dividendYieldModel, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYieldModel">Dividend yield model</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, IDividendYieldModel dividendYieldModel, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: this($"Theta({option},{mirrorOption},{GetOptionModel(optionModel, option.ID.OptionStyle)})", option, riskFreeRateModel,
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dividendYieldModel, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="name">The name of this indicator</param>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYieldModel">Dividend yield model</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(string name, Symbol option, PyObject riskFreeRateModel, PyObject dividendYieldModel, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRateModel, dividendYieldModel, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYieldModel">Dividend yield model</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(Symbol option, PyObject riskFreeRateModel, PyObject dividendYieldModel, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: this($"Theta({option},{mirrorOption},{GetOptionModel(optionModel, option.ID.OptionStyle)})", option, riskFreeRateModel,
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dividendYieldModel, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="name">The name of this indicator</param>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYield">Dividend yield, as a constant</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(string name, Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, decimal dividendYield = 0.0m, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRateModel, dividendYield, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYield">Dividend yield, as a constant</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, decimal dividendYield = 0.0m, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: this($"Theta({option},{mirrorOption},{GetOptionModel(optionModel, option.ID.OptionStyle)})", option, riskFreeRateModel,
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dividendYield, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="name">The name of this indicator</param>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYield">Dividend yield, as a constant</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(string name, Symbol option, PyObject riskFreeRateModel, decimal dividendYield = 0.0m, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRateModel, dividendYield, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRateModel">Risk-free rate model</param>
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/// <param name="dividendYield">Dividend yield, as a constant</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(Symbol option, PyObject riskFreeRateModel, decimal dividendYield = 0.0m, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: this($"Theta({option},{mirrorOption},{GetOptionModel(optionModel, option.ID.OptionStyle)})", option, riskFreeRateModel,
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dividendYield, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="name">The name of this indicator</param>
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/// <param name="option">The option to be tracked</param>am>
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/// <param name="riskFreeRate">Risk-free rate, as a constant</param>
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/// <param name="dividendYield">Dividend yield, as a constant</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(string name, Symbol option, decimal riskFreeRate = 0.05m, decimal dividendYield = 0.0m, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRate, dividendYield, mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Theta class
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/// </summary>
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/// <param name="option">The option to be tracked</param>
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/// <param name="riskFreeRate">Risk-free rate, as a constant</param>
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/// <param name="dividendYield">Dividend yield, as a constant</param>
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/// <param name="mirrorOption">The mirror option for parity calculation</param>
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/// <param name="optionModel">The option pricing model used to estimate Theta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Theta(Symbol option, decimal riskFreeRate = 0.05m, decimal dividendYield = 0.0m, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: this($"Theta({option},{mirrorOption},{GetOptionModel(optionModel, option.ID.OptionStyle)})", option, riskFreeRate, dividendYield,
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mirrorOption, optionModel, ivModel)
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{
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}
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/// <summary>
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/// Calculate the Theta of the option
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/// </summary>
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protected override decimal CalculateGreek(decimal timeTillExpiry)
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{
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var underlyingPrice = (double)UnderlyingPrice.Current.Value;
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var strike = (double)Strike;
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var timeTillExpiryDouble = (double)timeTillExpiry;
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var riskFreeRate = (double)RiskFreeRate.Current.Value;
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var dividendYield = (double)DividendYield.Current.Value;
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var iv = (double)ImpliedVolatility.Current.Value;
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double result;
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switch (_optionModel)
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{
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case OptionPricingModelType.BinomialCoxRossRubinstein:
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case OptionPricingModelType.ForwardTree:
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var deltaTime = timeTillExpiryDouble / OptionGreekIndicatorsHelper.Steps;
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var forwardPrice = 0d;
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var price = 0d;
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if (_optionModel == OptionPricingModelType.BinomialCoxRossRubinstein)
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{
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forwardPrice = OptionGreekIndicatorsHelper.CRRTheoreticalPrice(iv, underlyingPrice, strike, timeTillExpiryDouble - 2 * deltaTime, riskFreeRate, dividendYield, Right);
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price = OptionGreekIndicatorsHelper.CRRTheoreticalPrice(iv, underlyingPrice, strike, timeTillExpiryDouble, riskFreeRate, dividendYield, Right);
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}
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else if (_optionModel == OptionPricingModelType.ForwardTree)
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{
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forwardPrice = OptionGreekIndicatorsHelper.ForwardTreeTheoreticalPrice(iv, underlyingPrice, strike, timeTillExpiryDouble - 2 * deltaTime, riskFreeRate, dividendYield, Right);
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price = OptionGreekIndicatorsHelper.ForwardTreeTheoreticalPrice(iv, underlyingPrice, strike, timeTillExpiryDouble, riskFreeRate, dividendYield, Right);
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}
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result = (forwardPrice - price) * 0.5 / deltaTime / 365d;
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break;
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case OptionPricingModelType.BlackScholes:
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default:
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var norm = new Normal();
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var d1 = OptionGreekIndicatorsHelper.CalculateD1(underlyingPrice, strike, timeTillExpiryDouble, riskFreeRate, dividendYield, iv);
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var d2 = OptionGreekIndicatorsHelper.CalculateD2(d1, iv, timeTillExpiryDouble);
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var discount = Math.Exp(-riskFreeRate * timeTillExpiryDouble);
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var adjustment = Math.Exp(-dividendYield * timeTillExpiryDouble);
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// allow at least 1% IV
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var theta = -underlyingPrice * Math.Max(iv, 0.01) * norm.Density(d1) * adjustment * 0.5 / Math.Sqrt(timeTillExpiryDouble);
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if (Right == OptionRight.Call)
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{
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d1 = norm.CumulativeDistribution(d1);
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d2 = -norm.CumulativeDistribution(d2);
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}
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else
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{
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d1 = -norm.CumulativeDistribution(-d1);
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d2 = norm.CumulativeDistribution(-d2);
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}
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theta += dividendYield * underlyingPrice * d1 * adjustment + riskFreeRate * strike * discount * d2;
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result = theta / 365;
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break;
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}
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return Convert.ToDecimal(result);
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}
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}
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}
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