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Option Delta Indicator (#7704)
* 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
1 parent 00e1cae commit 3a10afe

11 files changed

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-278
lines changed

‎Algorithm/QCAlgorithm.Indicators.cs

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@@ -528,6 +528,48 @@ public DonchianChannel DCH(Symbol symbol, int period, Resolution? resolution = n
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return DCH(symbol, period, period, resolution, selector);
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}
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/// <summary>
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/// Creates a new Delta indicator for the symbol The indicator will be automatically
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/// updated on the symbol's subscription resolution
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/// </summary>
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/// <param name="symbol">The option symbol whose values we want as an indicator</param>
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/// <param name="riskFreeRate">The risk free rate</param>
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/// <param name="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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/// <param name="resolution">The desired resolution of the data</param>
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/// <returns>A new Delta indicator for the specified symbol</returns>
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[DocumentationAttribute(Indicators)]
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public Delta D(Symbol symbol, decimal? riskFreeRate = null, OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes,
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OptionPricingModelType? ivModel = null, Resolution? resolution = null)
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{
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var name = CreateIndicatorName(symbol, $"Delta({riskFreeRate},{optionModel},{ivModel})", resolution);
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IRiskFreeInterestRateModel riskFreeRateModel = riskFreeRate.HasValue
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? new ConstantRiskFreeRateInterestRateModel(riskFreeRate.Value)
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// Make it a function so it's lazily evaluated: SetRiskFreeInterestRateModel can be called after this method
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: new FuncRiskFreeRateInterestRateModel((datetime) => RiskFreeInterestRateModel.GetInterestRate(datetime));
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var delta = new Delta(name, symbol, riskFreeRateModel, optionModel, ivModel);
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RegisterIndicator(symbol, delta, ResolveConsolidator(symbol, resolution));
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RegisterIndicator(symbol.Underlying, delta, ResolveConsolidator(symbol, resolution));
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return delta;
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}
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/// <summary>
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/// Creates a new Delta indicator for the symbol The indicator will be automatically
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/// updated on the symbol's subscription resolution
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/// </summary>
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/// <param name="symbol">The option symbol whose values we want as an indicator</param>
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/// <param name="riskFreeRate">The risk free rate</param>
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/// <param name="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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/// <param name="resolution">The desired resolution of the data</param>
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/// <returns>A new Delta indicator for the specified symbol</returns>
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[DocumentationAttribute(Indicators)]
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public Delta Δ(Symbol symbol, decimal? riskFreeRate = null, OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes,
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OptionPricingModelType? ivModel = null, Resolution? resolution = null)
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{
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return D(symbol, riskFreeRate, optionModel, ivModel, resolution);
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}
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/// <summary>
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/// Creates a new DoubleExponentialMovingAverage indicator.
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/// </summary>

‎Indicators/Delta.cs

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@@ -0,0 +1,157 @@
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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 Delta indicator that calculate the delta of an option
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/// </summary>
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/// <remarks>sensitivity of option price relative to $1 of underlying change</remarks>
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public class Delta : OptionGreeksIndicatorBase
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{
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/// <summary>
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/// Initializes a new instance of the Delta 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="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Delta(string name, Symbol option, IRiskFreeInterestRateModel riskFreeRateModel,
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OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRateModel, optionModel: optionModel, ivModel: ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Delta 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="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Delta(Symbol option, IRiskFreeInterestRateModel riskFreeRateModel,
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OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null)
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: this($"Delta({optionModel})", option, riskFreeRateModel, 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 Delta 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="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Delta(string name, Symbol option, PyObject riskFreeRateModel,
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OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRateModel, optionModel: optionModel, ivModel: ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Delta 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="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Delta(Symbol option, PyObject riskFreeRateModel, OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes,
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OptionPricingModelType? ivModel = null)
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: this($"Delta({optionModel})", option, riskFreeRateModel, 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 Delta class
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/// </summary>
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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="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Delta(string name, Symbol option, decimal riskFreeRate = 0.05m,
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OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes, OptionPricingModelType? ivModel = null)
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: base(name, option, riskFreeRate, optionModel: optionModel, ivModel: ivModel)
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{
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}
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/// <summary>
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/// Initializes a new instance of the Delta 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="optionModel">The option pricing model used to estimate Delta</param>
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/// <param name="ivModel">The option pricing model used to estimate IV</param>
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public Delta(Symbol option, decimal riskFreeRate = 0.05m, OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes,
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OptionPricingModelType? ivModel = null)
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: this($"Delta({optionModel})", option, riskFreeRate, optionModel, ivModel)
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{
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}
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// Calculate the theoretical option price
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private decimal TheoreticalDelta(decimal spotPrice, decimal timeToExpiration, decimal volatility,
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OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes)
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{
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var math = OptionGreekIndicatorsHelper.DecimalMath;
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switch (optionModel)
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{
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case OptionPricingModelType.BinomialCoxRossRubinstein:
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var upFactor = math(Math.Exp, volatility * math(Math.Sqrt, timeToExpiration / OptionGreekIndicatorsHelper.Steps));
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if (upFactor == 1)
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{
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// provide a small step to estimate delta
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upFactor = 1.00001m;
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}
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var sU = spotPrice * upFactor;
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var sD = spotPrice * 1m / upFactor;
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var fU = OptionGreekIndicatorsHelper.CRRTheoreticalPrice(volatility, sU, Strike, timeToExpiration, RiskFreeRate, Right);
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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:
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default:
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var norm = new Normal();
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var d1 = OptionGreekIndicatorsHelper.CalculateD1(spotPrice, Strike, timeToExpiration, RiskFreeRate, volatility);
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if (Right == OptionRight.Call)
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{
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return math(norm.CumulativeDistribution, d1);
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}
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return -math(norm.CumulativeDistribution, -d1);
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}
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}
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// Calculate the Delta of the option
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protected override decimal CalculateGreek(DateTime time)
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{
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var spotPrice = UnderlyingPrice.Current.Value;
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var timeToExpiration = Convert.ToDecimal((Expiry - time).TotalDays) / 365m;
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var volatility = ImpliedVolatility.Current.Value;
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return TheoreticalDelta(spotPrice, timeToExpiration, volatility, _optionModel);
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}
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}
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}

‎Indicators/ImpliedVolatility.cs

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@@ -26,60 +26,17 @@ namespace QuantConnect.Indicators
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/// <summary>
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/// Implied Volatility indicator that calculate the IV of an option using Black-Scholes Model
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/// </summary>
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public class ImpliedVolatility : IndicatorBase<IndicatorDataPoint>, IIndicatorWarmUpPeriodProvider
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public class ImpliedVolatility : OptionIndicatorBase
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{
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private readonly Symbol _optionSymbol;
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private readonly Symbol _underlyingSymbol;
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private BaseDataConsolidator _consolidator;
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private RateOfChange _roc;
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private decimal _impliedVolatility;
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private OptionPricingModelType _optionModel;
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/// <summary>
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/// Risk-free rate model
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/// </summary>
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private readonly IRiskFreeInterestRateModel _riskFreeInterestRateModel;
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/// <summary>
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/// Gets the expiration time of the option
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/// </summary>
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public DateTime Expiry => _optionSymbol.ID.Date;
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/// <summary>
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/// Gets the option right (call/put) of the option
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/// </summary>
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public OptionRight Right => _optionSymbol.ID.OptionRight;
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/// <summary>
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/// Gets the strike price of the option
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/// </summary>
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public decimal Strike => _optionSymbol.ID.StrikePrice;
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/// <summary>
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/// Gets the option style (European/American) of the option
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/// </summary>
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public OptionStyle Style => _optionSymbol.ID.OptionStyle;
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/// <summary>
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/// Risk Free Rate
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/// </summary>
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public Identity RiskFreeRate { get; set; }
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/// <summary>
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/// Gets the historical volatility of the underlying
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/// </summary>
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public IndicatorBase<IndicatorDataPoint> HistoricalVolatility { get; }
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/// <summary>
74-
/// Gets the option price level
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/// </summary>
76-
public IndicatorBase<IndicatorDataPoint> Price { get; }
77-
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/// <summary>
79-
/// Gets the underlying's price level
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/// </summary>
81-
public IndicatorBase<IndicatorDataPoint> UnderlyingPrice { get; }
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8340
/// <summary>
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/// Initializes a new instance of the ImpliedVolatility class
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/// </summary>
@@ -90,37 +47,21 @@ public class ImpliedVolatility : IndicatorBase<IndicatorDataPoint>, IIndicatorWa
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/// <param name="optionModel">The option pricing model used to estimate IV</param>
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public ImpliedVolatility(string name, Symbol option, IRiskFreeInterestRateModel riskFreeRateModel, int period = 252,
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OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes)
93-
: base(name)
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: base(name, option, riskFreeRateModel, period, optionModel)
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{
95-
var sid = option.ID;
96-
if (!sid.SecurityType.IsOption())
97-
{
98-
throw new ArgumentException("ImpliedVolatility only support SecurityType.Option.");
99-
}
100-
101-
_optionSymbol = option;
102-
_underlyingSymbol = option.Underlying;
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_roc = new(1);
104-
_riskFreeInterestRateModel = riskFreeRateModel;
105-
_optionModel = optionModel;
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RiskFreeRate = new Identity(name + "_RiskFreeRate");
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HistoricalVolatility = IndicatorExtensions.Times(
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IndicatorExtensions.Of(
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new StandardDeviation(period),
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_roc
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),
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Convert.ToDecimal(Math.Sqrt(252))
11459
);
115-
Price = new Identity(name + "_Close");
116-
UnderlyingPrice = new Identity(name + "_UnderlyingClose");
117-
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11861
_consolidator = new(TimeSpan.FromDays(1));
11962
_consolidator.DataConsolidated += (_, bar) => {
12063
_roc.Update(bar.EndTime, bar.Price);
12164
};
122-
123-
WarmUpPeriod = period;
12465
}
12566

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/// <summary>
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/// <param name="optionModel">The option pricing model used to estimate IV</param>
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public ImpliedVolatility(Symbol option, PyObject riskFreeRateModel, int period = 252,
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OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes)
162-
: this($"IV({option.Value},{period},{optionModel})", option,
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RiskFreeInterestRateModelPythonWrapper.FromPyObject(riskFreeRateModel), period, optionModel)
103+
: this($"IV({option.Value},{period},{optionModel})", option, riskFreeRateModel, period, optionModel)
164104
{
165105
}
166106

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187127
/// <param name="optionModel">The option pricing model used to estimate IV</param>
188128
public ImpliedVolatility(Symbol option, decimal riskFreeRate = 0.05m, int period = 252,
189129
OptionPricingModelType optionModel = OptionPricingModelType.BlackScholes)
190-
: this($"IV({option.Value},{period},{riskFreeRate},{optionModel})", option,
191-
new ConstantRiskFreeRateInterestRateModel(riskFreeRate), period, optionModel)
130+
: this($"IV({option.Value},{period},{riskFreeRate},{optionModel})", option, riskFreeRate, period, optionModel)
192131
{
193132
}
194133

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197136
/// </summary>
198137
public override bool IsReady => HistoricalVolatility.Samples >= 2 && Price.Current.Time == UnderlyingPrice.Current.Time;
199138

200-
/// <summary>
201-
/// Required period, in data points, for the indicator to be ready and fully initialized.
202-
/// </summary>
203-
public int WarmUpPeriod { get; }
204-
205139
/// <summary>
206140
/// Computes the next value
207141
/// </summary>
@@ -281,10 +215,7 @@ public override void Reset()
281215
};
282216

283217
_roc.Reset();
284-
RiskFreeRate.Reset();
285218
HistoricalVolatility.Reset();
286-
Price.Reset();
287-
UnderlyingPrice.Reset();
288219
base.Reset();
289220
}
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}

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