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 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 Rho indicator that calculate the rho of an option
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/// </summary>
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/// <remarks>sensitivity of option price on interest rate changes</remarks>
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public class Rho : OptionGreeksIndicatorBase
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{
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/// <summary>
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/// Initializes a new instance of the Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, IDividendYieldModel dividendYieldModel, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: this($"Rho({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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(Symbol option, PyObject riskFreeRateModel, PyObject dividendYieldModel, Symbol mirrorOption = null,
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OptionPricingModelType? optionModel = null, OptionPricingModelType? ivModel = null)
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: this($"Rho({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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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($"Rho({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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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($"Rho({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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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 Rho 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 Rho</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Rho(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($"Rho({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 Rho 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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// finite differencing method with 0.01% risk free rate changes
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var deltaRho = 0.0001;
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var newPrice = 0d;
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var price = 0d;
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if (_optionModel == OptionPricingModelType.BinomialCoxRossRubinstein)
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{
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newPrice = OptionGreekIndicatorsHelper.CRRTheoreticalPrice(iv, underlyingPrice, strike, timeTillExpiryDouble, riskFreeRate + deltaRho, 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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newPrice = OptionGreekIndicatorsHelper.ForwardTreeTheoreticalPrice(iv, underlyingPrice, strike, timeTillExpiryDouble, riskFreeRate + deltaRho, 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 = (newPrice - price) / deltaRho / 100d;
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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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if (Right == OptionRight.Call)
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{
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result = strike * timeTillExpiryDouble * discount * norm.CumulativeDistribution(d2) / 100d;
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}
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else
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{
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result = -strike * timeTillExpiryDouble * discount * norm.CumulativeDistribution(-d2) / 100d;
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}
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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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