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* Add base indicator for greeks * Add option delta indicator * Add helper method * Add unit tests * Address peer review * Fix minor bugs * Change OptionDelta into Delta * rename helper method
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| /* | ||
| * QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals. | ||
| * Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation. | ||
| * | ||
| * Licensed under the Apache License, Version 2.0 (the "License"); | ||
| * you may not use this file except in compliance with the License. | ||
| * You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 | ||
| * | ||
| * Unless required by applicable law or agreed to in writing, software | ||
| * distributed under the License is distributed on an "AS IS" BASIS, | ||
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
| * See the License for the specific language governing permissions and | ||
| * limitations under the License. | ||
| */ | ||
|
|
||
| using System; | ||
| using MathNet.Numerics.Distributions; | ||
| using Python.Runtime; | ||
| using QuantConnect.Data; | ||
|
|
||
| namespace QuantConnect.Indicators | ||
| { | ||
| /// <summary> | ||
| /// Option Delta indicator that calculate the delta of an option | ||
| /// </summary> | ||
| /// <remarks>sensitivity of option price relative to $1 of underlying change</remarks> | ||
| public class Delta : OptionGreeksIndicatorBase | ||
| { | ||
| /// <summary> | ||
| /// Initializes a new instance of the Delta class | ||
| /// </summary> | ||
| /// <param name="name">The name of this indicator</param> | ||
| /// <param name="option">The option to be tracked</param> | ||
| /// <param name="riskFreeRateModel">Risk-free rate model</param> | ||
| /// <param name="optionModel">The option pricing model used to estimate Delta</param> | ||
| /// <param name="ivModel">The option pricing model used to estimate IV</param> | ||
| public Delta(string name, Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, | ||
| OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null) | ||
| : base(name, option, riskFreeRateModel, optionModel: optionModel, ivModel: ivModel) | ||
| { | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Initializes a new instance of the Delta class | ||
| /// </summary> | ||
| /// <param name="option">The option to be tracked</param> | ||
| /// <param name="riskFreeRateModel">Risk-free rate model</param> | ||
| /// <param name="optionModel">The option pricing model used to estimate Delta</param> | ||
| /// <param name="ivModel">The option pricing model used to estimate IV</param> | ||
| public Delta(Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, | ||
| OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null) | ||
| : this($"Delta({optionModel})", option, riskFreeRateModel, optionModel, ivModel) | ||
| { | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Initializes a new instance of the Delta class | ||
| /// </summary> | ||
| /// <param name="name">The name of this indicator</param> | ||
| /// <param name="option">The option to be tracked</param> | ||
| /// <param name="riskFreeRateModel">Risk-free rate model</param> | ||
| /// <param name="optionModel">The option pricing model used to estimate Delta</param> | ||
| /// <param name="ivModel">The option pricing model used to estimate IV</param> | ||
| public Delta(string name, Symbol option, PyObject riskFreeRateModel, | ||
| OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null) | ||
| : base(name, option, riskFreeRateModel, optionModel: optionModel, ivModel: ivModel) | ||
| { | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Initializes a new instance of the Delta class | ||
| /// </summary> | ||
| /// <param name="option">The option to be tracked</param> | ||
| /// <param name="riskFreeRateModel">Risk-free rate model</param> | ||
| /// <param name="optionModel">The option pricing model used to estimate Delta</param> | ||
| /// <param name="ivModel">The option pricing model used to estimate IV</param> | ||
| public Delta(Symbol option, PyObject riskFreeRateModel, OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, | ||
| OptionPricingModelType? ivModel = null) | ||
| : this($"Delta({optionModel})", option, riskFreeRateModel, optionModel, ivModel) | ||
| { | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Initializes a new instance of the Delta class | ||
| /// </summary> | ||
| /// <param name="option">The option to be tracked</param>am> | ||
| /// <param name="riskFreeRate">Risk-free rate, as a constant</param> | ||
| /// <param name="optionModel">The option pricing model used to estimate Delta</param> | ||
| /// <param name="ivModel">The option pricing model used to estimate IV</param> | ||
| public Delta(string name, Symbol option, decimal riskFreeRate = 0.05m, | ||
| OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null) | ||
| : base(name, option, riskFreeRate, optionModel: optionModel, ivModel: ivModel) | ||
| { | ||
| } | ||
|
|
||
| /// <summary> | ||
| /// Initializes a new instance of the Delta class | ||
| /// </summary> | ||
| /// <param name="option">The option to be tracked</param> | ||
| /// <param name="riskFreeRate">Risk-free rate, as a constant</param> | ||
| /// <param name="optionModel">The option pricing model used to estimate Delta</param> | ||
| /// <param name="ivModel">The option pricing model used to estimate IV</param> | ||
| public Delta(Symbol option, decimal riskFreeRate = 0.05m, OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, | ||
| OptionPricingModelType? ivModel = null) | ||
| : this($"Delta({optionModel})", option, riskFreeRate, optionModel, ivModel) | ||
| { | ||
| } | ||
|
|
||
| // Calculate the theoretical option price | ||
| private decimal TheoreticalDelta(decimal spotPrice, decimal timeToExpiration, decimal volatility, | ||
| OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes) | ||
| { | ||
| var math = OptionGreekIndicatorsHelper.DecimalMath; | ||
|
|
||
| switch (optionModel) | ||
| { | ||
| case OptionPricingModelType.BinomialCoxRossRubinstein: | ||
| var upFactor = math(Math.Exp, volatility * math(Math.Sqrt, timeToExpiration / OptionGreekIndicatorsHelper.Steps)); | ||
| if (upFactor == 1) | ||
| { | ||
| // provide a small step to estimate delta | ||
| upFactor = 1.00001m; | ||
| } | ||
|
|
||
| var sU = spotPrice * upFactor; | ||
| var sD = spotPrice * 1m / upFactor; | ||
|
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||
| var fU = OptionGreekIndicatorsHelper.CRRTheoreticalPrice(volatility, sU, Strike, timeToExpiration, RiskFreeRate, Right); | ||
| var fD = OptionGreekIndicatorsHelper.CRRTheoreticalPrice(volatility, sD, Strike, timeToExpiration, RiskFreeRate, Right); | ||
|
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| return (fU - fD) / (sU - sD); | ||
|
|
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| case OptionPricingModelType.BlackScholes: | ||
| default: | ||
| var norm = new Normal(); | ||
| var d1 = OptionGreekIndicatorsHelper.CalculateD1(spotPrice, Strike, timeToExpiration, RiskFreeRate, volatility); | ||
|
|
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| if (Right == OptionRight.Call) | ||
| { | ||
| return math(norm.CumulativeDistribution, d1); | ||
| } | ||
|
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| return -math(norm.CumulativeDistribution, -d1); | ||
| } | ||
| } | ||
|
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| // Calculate the Delta of the option | ||
| protected override decimal CalculateGreek(DateTime time) | ||
| { | ||
| var spotPrice = UnderlyingPrice.Current.Value; | ||
| var timeToExpiration = Convert.ToDecimal((Expiry - time).TotalDays) / 365m; | ||
| var volatility = ImpliedVolatility.Current.Value; | ||
|
|
||
| return TheoreticalDelta(spotPrice, timeToExpiration, volatility, _optionModel); | ||
| } | ||
| } | ||
| } |
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