public HestonCallSimulationOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound) : base(equityCalData, matBound, strikeBound) { //this.dyFunc = equityCalData.dyFunc; this.dyFunc = CallEstimator.IstantaneousDividendYield(equityCalData); this.zrFunc = equityCalData.zrFunc; // Generates common random numbers I = (int)Math.Ceiling(cpmd.Maturity[Range.End] / dt); epsilon = new Matrix(I, 2 * N); NewRandomNumbers(); // Precalculates istantaneous growth rates growth = new Vector(I); for (int i = 0; i < I; i++) { double t = i * dt; double zr_t = zrFunc.Evaluate(t); growth[i] = zr_t + FunctionHelper.Partial(zr_t, zrFunc, new Vector() { t }, 0, dt) * t - dyFunc.Evaluate(t); } Console.WriteLine("Heston Simulation Calibration: Paths=" + N); }
double DY(EquityCalibrationData equityCalData) { double dy = 0.5 * (equityCalData.dyFunc.Evaluate(1) + equityCalData.dyFunc.Evaluate(2)); Console.WriteLine("Call/Put Parity Dividend\t" + dy); return(dy); }
internal static IFunction IstantaneousDividendYield(EquityCalibrationData ecd) { double support = Math.Min(6, Math.Max(2, (ecd.dyFunc as PFunction).Support[Range.End])); var avgDy = new GBM.FunctionParamPiecewiseConstant(support, 0);//positive f. (avgDy as GBM.FunctionParamBase).FitToMean(ecd.dyFunc, 0, support); return(avgDy); }
/// <summary> /// Initializes a new instance of the HestonCallOptimizationProblem class using the /// EquityCalibrationData data structure. /// </summary> /// <param name="equityCalData"> /// An EquityCalibrationData object containing market data for calibration. /// </param> /// <param name="matBound"> /// A vector containing the minimum and maximum values /// for maturities to be used in calibration. /// </param> /// <param name="strikeBound"> /// A vector containing the minimum and maximum values /// for strikes to be used in calibration. /// </param> public HestonCallOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound) { this.cpmd = equityCalData.Hdata; this.matBound = matBound; this.strikeBound = strikeBound; SetVariables(equityCalData.Hdata.CallPrice, equityCalData.Hdata.Maturity, equityCalData.Hdata.Strike, equityCalData.CallMatrixRiskFreeRate, equityCalData.CallMatrixDividendYield, equityCalData.Hdata.S0); displayObjInfo = false; }
private EstimationResult FairmatEstimate(CurveMarketData discountingCurve, CallPriceMarketData Hdataset) { EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discountingCurve); //HCalData.Setup(Hdataset, discountingCurve); bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2); if (hasArbitrage) { Console.WriteLine("Market data contains arbitrage opportunity"); } this.r = new DVPLDOM.PFunction(discountingCurve.Durations, discountingCurve.Values); this.q = HCalData.dyFunc as PFunction; //this.q.Expr = (double[,])ArrayHelper.Concat(HCalData.MaturityDY.ToArray(), HCalData.DividendYield.ToArray()); this.r.Parse(null); this.q.Parse(null); Vector locVolMat, locVolStr; //IFunction fittedSurface = FitImplVolModel(Hdataset); //Matrix locVolMatrix = LocVolMatrixFromImpliedVol(Hdataset, fittedSurface, out locVolMat, out locVolStr); CallPriceSurface fittedSurface = CallPriceSurface.NoArbitrageSurface(HCalData); Matrix locVolMatrix = LocVolMatrixFromCallPrices(Hdataset, fittedSurface, out locVolMat, out locVolStr); Console.WriteLine(locVolMatrix); // Create dupire outputs. PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix); localVol.Parse(null); string[] names = new string[] { "S0" }; Vector param = new Vector(1); param[0] = Hdataset.S0; EstimationResult result = new EstimationResult(names, param); //result.Objects = new object[3]; result.Objects = new object[4]; result.Objects[0] = this.r; result.Objects[1] = this.q; result.Objects[2] = localVol; result.Objects[3] = fittedSurface; //Console.WriteLine("r = " + HCalData.Rate.ToString()); //Console.WriteLine("q = " + HCalData.DividendYield.ToString()); return(result); }
/// <summary> /// Attempts to solve the Variance Gamma Optimization problem using /// <see cref="Heston.VarianceGammaOptimizationProblem"/>. /// </summary> /// <param name="data"> /// The data to be used in order to perform the optimization. /// </param> /// <param name="settings">The parameter is not used.</param> /// <returns>The results of the optimization.</returns> public EstimationResult Estimate(List <object> data, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null) { EquitySpotMarketData espmd = data[0] as EquitySpotMarketData; CallPriceMarketData cpmd = data[1] as CallPriceMarketData; DiscountingCurveMarketData dcmd = data[2] as DiscountingCurveMarketData; EquityCalibrationData ecd = new EquityCalibrationData(cpmd, dcmd); this.s0 = espmd.Price; this.r = espmd.RiskFreeRate; this.q = espmd.DividendYield; this.k = ecd.Hdata.Strike; this.m = ecd.Hdata.Maturity; this.cp = ecd.Hdata.CallPrice; Vector x0 = (Vector) new double[] { -0.1, 0.2, 0.1 }; IOptimizationAlgorithm algorithm = new QADE(); OptimizationSettings optimizationSettings = new DESettings(); // Maximum number of iteration allowed. // Positive integer values print debug info. optimizationSettings.Verbosity = 1; // Tolerance. optimizationSettings.epsilon = 10e-5; var solution = algorithm.Minimize(new VarianceGammaOptimizationProblem(this.q, this.s0, this.k, this.r, this.cp, this.m), optimizationSettings, x0); if (solution.errors) { return(new EstimationResult(solution.message)); } var er = new EstimationResult(); er.Names = new string[] { "S0", "theta", "sigma", "nu", "rate", "dividend" }; er.Values = new double[] { this.s0, solution.x[0], solution.x[1], solution.x[2], this.r, this.q }; return(er); }
protected override void Setup(EquityCalibrationData equityCalData, IEstimationSettings settings) { //No need to used constant values. In the optimization procedure we can use the term structure //as it is. /* * //equityCalData.dyFunc= LeastSquaresDividendCalibration(equityCalData.Hdata, equityCalData.zrFunc); * * if (settings != null) //uses settings if provided. * { * var localSettings = (HestonEstimationSettings)settings; * * equityCalData.SetToSpecificMaturity(localSettings.Maturity); * } * else * equityCalData.SetToSpecificMaturity(1); */ DY(equityCalData); return; }
public HestonCallSimulationOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound) : base(equityCalData,matBound,strikeBound) { //this.dyFunc = equityCalData.dyFunc; this.dyFunc = CallEstimator.IstantaneousDividendYield(equityCalData); this.zrFunc = equityCalData.zrFunc; // Generates common random numbers I = (int)Math.Ceiling(cpmd.Maturity[Range.End] / dt); epsilon = new Matrix(I, 2*N); NewRandomNumbers(); // Precalculates istantaneous growth rates growth = new Vector(I); for (int i = 0; i < I; i++) { double t = i * dt; double zr_t = zrFunc.Evaluate(t); growth[i] = zr_t + FunctionHelper.Partial(zr_t,zrFunc, new Vector() { t }, 0, dt) * t - dyFunc.Evaluate(t); } Console.WriteLine("Heston Simulation Calibration: Paths=" + N); }
protected virtual void Setup(EquityCalibrationData equityCalData, IEstimationSettings settings) { }
protected override EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution) { string[] names = new string[] { "S0", "kappa", "theta", "sigma", "rho", "V0", "r", "q" }; Vector param = new Vector(8); param[0] = spotPrice.Value; param[Range.New(1, 5)] = solution.x[Range.New(0, 4)]; param[6] = equityCalData.zrFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity); if (impliedDividends) { param[7] = solution.x[Range.End];// equityCalData.dyFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity); } else { param[7] = DY(equityCalData); } var result = new EstimationResult(names, param); result.Fit = HestonCallOptimizationProblem.avgPricingError; Console.WriteLine(result); return(result); }
protected virtual EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution) { string[] names = new string[] { "S0", "kappa", "theta", "sigma", "rho", "V0" }; Vector param = new Vector(6); param[0] = spotPrice.Value; param[Range.New(1, 5)] = solution.x; var result = new EstimationResult(names, param); // In the following the two function describing the ZR and dividend yields are created //Matrix zerorate = new Matrix(interestDataSet.Durations.Length, 2); //zerorate[Range.All, 0] = interestDataSet.Durations; //zerorate[Range.All, 1] = interestDataSet.Values; //Matrix dividendYield = new Matrix(equityCalData.MaturityDY.Length, 2); //dividendYield[Range.All, 0] = equityCalData.MaturityDY; //dividendYield[Range.All, 1] = equityCalData.DividendYield; Matrix zerorate = new Matrix((equityCalData.zrFunc as PFunction).Expr); //Matrix dividendYield = new Matrix((equityCalData.dyFunc as PFunction).Expr); Matrix dividendYield = ToMatrix(IstantaneousDividendYield(equityCalData)); result.Objects = new object[2]; result.Objects[0] = zerorate; result.Objects[1] = dividendYield; result.Fit = solution.obj; Console.WriteLine(result); return(result); }
/// <summary> /// Attempts to solve the Variance Gamma Optimization problem using /// <see cref="Heston.VarianceGammaOptimizationProblem"/>. /// </summary> /// <param name="data"> /// The data to be used in order to perform the optimization. /// </param> /// <param name="settings">The parameter is not used.</param> /// <returns>The results of the optimization.</returns> public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null) { EquitySpotMarketData espmd = data[0] as EquitySpotMarketData; CallPriceMarketData cpmd = data[1] as CallPriceMarketData; DiscountingCurveMarketData dcmd = data[2] as DiscountingCurveMarketData; EquityCalibrationData ecd = new EquityCalibrationData(cpmd, dcmd); this.s0 = espmd.Price; this.r = espmd.RiskFreeRate; this.q = espmd.DividendYield; this.k = ecd.Hdata.Strike; this.m = ecd.Hdata.Maturity; this.cp = ecd.Hdata.CallPrice; Vector x0 = (Vector)new double[] { -0.1, 0.2, 0.1 }; IOptimizationAlgorithm algorithm = new QADE(); OptimizationSettings optimizationSettings = new DESettings(); // Maximum number of iteration allowed. // Positive integer values print debug info. optimizationSettings.Verbosity = 1; // Tolerance. optimizationSettings.epsilon = 10e-5; var solution = algorithm.Minimize(new VarianceGammaOptimizationProblem(this.q, this.s0, this.k, this.r, this.cp, this.m), optimizationSettings, x0); if (solution.errors) return new EstimationResult(solution.message); var er = new EstimationResult(); er.Names= new string[]{"S0","theta","sigma","nu","rate","dividend"}; er.Values = new double[] {this.s0,solution.x[0],solution.x[1],solution.x[2],this.r,this.q}; return er; }
internal static IFunction IstantaneousDividendYield(EquityCalibrationData ecd) { double support = Math.Min(6, Math.Max(2, (ecd.dyFunc as PFunction).Support[Range.End])); var avgDy = new GBM.FunctionParamPiecewiseConstant(support, 0);//positive f. (avgDy as GBM.FunctionParamBase).FitToMean(ecd.dyFunc, 0, support); return avgDy; }
double DY(EquityCalibrationData equityCalData) { double dy= 0.5*(equityCalData.dyFunc.Evaluate(1) + equityCalData.dyFunc.Evaluate(2)); Console.WriteLine("Call/Put Parity Dividend\t" + dy); return dy; }
protected override HestonCallOptimizationProblem NewOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound) { return new HestonCallSimulationOptimizationProblem(equityCalData, matBound, strikeBound); }
private EstimationResult FairmatEstimate(CurveMarketData discountingCurve, CallPriceMarketData Hdataset) { EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discountingCurve); //HCalData.Setup(Hdataset, discountingCurve); bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2); if (hasArbitrage) Console.WriteLine("Market data contains arbitrage opportunity"); this.r = new DVPLDOM.PFunction(discountingCurve.Durations,discountingCurve.Values); this.q = HCalData.dyFunc as PFunction; //this.q.Expr = (double[,])ArrayHelper.Concat(HCalData.MaturityDY.ToArray(), HCalData.DividendYield.ToArray()); this.r.Parse(null); this.q.Parse(null); Vector locVolMat, locVolStr; //IFunction fittedSurface = FitImplVolModel(Hdataset); //Matrix locVolMatrix = LocVolMatrixFromImpliedVol(Hdataset, fittedSurface, out locVolMat, out locVolStr); CallPriceSurface fittedSurface = CallPriceSurface.NoArbitrageSurface(HCalData); Matrix locVolMatrix = LocVolMatrixFromCallPrices(Hdataset, fittedSurface, out locVolMat, out locVolStr); Console.WriteLine(locVolMatrix); // Create dupire outputs. PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix); localVol.Parse(null); string[] names = new string[] { "S0" }; Vector param = new Vector(1); param[0] = Hdataset.S0; EstimationResult result = new EstimationResult(names, param); //result.Objects = new object[3]; result.Objects = new object[4]; result.Objects[0] = this.r; result.Objects[1] = this.q; result.Objects[2] = localVol; result.Objects[3] = fittedSurface; //Console.WriteLine("r = " + HCalData.Rate.ToString()); //Console.WriteLine("q = " + HCalData.DividendYield.ToString()); return result; }
public static void Main(string[] args) { int Caso = 1; if (Caso == 0) { InterestRateMarketData MData = InterestRateMarketData.FromFile("../../../TestData/InterestRatesModels/05052009-EU.xml"); CallPriceMarketData test = CallPriceMarketData.FromFile("../../../TestData/Heston/05052009-SX5E-HestonData.xml"); EquityCalibrationData CalData = new EquityCalibrationData(test, MData); Matrix CallMarketPrice = (Matrix)test.CallPrice; Vector Maturity = (Vector)test.Maturity; Vector Strike = (Vector)test.Strike; Vector DividendYield = (Vector)test.DividendYield; Vector Drift = CalData.Rate - CalData.DividendYield; Vector Rate = CalData.Rate; double u, kappa, theta, sigma, rho, v0, s0, r, q, T, K, val; u = 1.0; kappa = 19.4; theta = 0.235; sigma = 0.00500999; rho = -0.96; v0 = 0.664; s0 = 3872.15; r = -0.0867303549580581; q = 0; T = 0.50; K = 6000; Vector MatBound = new Vector(2); Vector StrikeBound = new Vector(2); MatBound[0] = 0.0; MatBound[1] = 2.0; StrikeBound[0] = 0.7; StrikeBound[1] = 1.3; Matrix Volatility = new Matrix(test.CallPrice.R, test.CallPrice.C); HestonCallOptimizationProblem HP = new HestonCallOptimizationProblem(CallMarketPrice, Maturity, Strike, Rate, DividendYield, test.S0, MatBound, StrikeBound, Volatility); Complex Cval, Cu; Cu = u - Complex.I; HestonCall hc = new HestonCall(HP); Cval = hc.phi(u, kappa, theta, sigma, rho, s0, v0, r, T); Console.WriteLine("phi1 = {0}", Cval); Cval = hc.phi(Cu, kappa, theta, sigma, rho, s0, v0, r, T); Console.WriteLine("phi2 = {0}", Cval); val = hc.IntegrandFunc(u, kappa, theta, sigma, rho, s0, v0, r, q, T, K); Console.WriteLine("IntFunc = {0}", val); Vector x = new Vector(5); x[0] = kappa; x[1] = theta; x[2] = sigma; x[3] = rho; x[4] = v0; DateTime T1, T2; TimeSpan ElapsedTime; double Time, Time2, Time3; T1 = DateTime.Now; val = hc.HestonCallPrice(x, s0, T, K, r, q); T2 = DateTime.Now; ElapsedTime = T2 - T1; Time = (double)ElapsedTime.Milliseconds; Time2 = (double)ElapsedTime.Seconds; Console.WriteLine("Price = {0}", val); Console.WriteLine("Elapsed Time = {0}", Time2 + Time / 1000); int NProve = 10; int NPassi = 1000; double val2; Random CasNum = new Random(); for (int i = 0; i < NProve; i++) { for (int j = 0; j < 5; j++) { val2 = ((double)CasNum.Next(0, NPassi)) / ((double)NPassi); x[j] = HP.Bounds.Lb[j] + (HP.Bounds.Ub[j] - HP.Bounds.Lb[j]) * val2; } Console.Write("Trial {0} x = " + x.ToString(), i + 1); T1 = DateTime.Now; val = HP.Obj(x); T2 = DateTime.Now; ElapsedTime = T2 - T1; Time = (double)ElapsedTime.Milliseconds; Time2 = (double)ElapsedTime.Seconds; Time3 = (double)ElapsedTime.Minutes; Console.WriteLine(" Time = {0}' {1}'' Val = {2}", Time3, Time2 + Time / 1000, val); } } if (Caso == 1) { TestHestonCallEstimation NewTest = new TestHestonCallEstimation(); bool Result = NewTest.Run(); } }
/// <summary> /// Attempts to solve the Heston optimization problem using /// <see cref="Heston.HestonOptimizationProblem"/>. /// </summary> /// <param name="marketData">Data to be used in order to perform the optimization.</param> /// <param name="settings">The parameter is not used.</param> /// <param name="controller">IController.</param> /// <returns>The results of the optimization.</returns> public EstimationResult Estimate(List<object> marketData, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null) { DateTime t0 = DateTime.Now; var interestDataSet = (CurveMarketData)marketData[0]; CallPriceMarketData callDataSet = (CallPriceMarketData)marketData[1]; EquityCalibrationData equityCalData = new EquityCalibrationData(callDataSet, interestDataSet); var spotPrice = (DVPLI.MarketDataTypes.Scalar)marketData[2]; Setup(equityCalData, settings); var calSettings = settings as HestonCalibrationSettings; // Creates the context. Document doc = new Document(); ProjectROV prj = new ProjectROV(doc); doc.Part.Add(prj); // Optimization problem instance. Vector matBound = new Vector(2); Vector strikeBound = new Vector(2); if (calSettings != null) { matBound[0] = calSettings.MinMaturity; matBound[1] = calSettings.MaxMaturity; strikeBound[0] = calSettings.MinStrike; strikeBound[1] = calSettings.MaxStrike; } else { //use defaults matBound[0] = 1.0 / 12;// .25; matBound[1] = 6;// 10; //Up to 6Y maturities strikeBound[0] = 0.4; strikeBound[1] = 1.6; } Console.WriteLine(callDataSet); /* //CBA TEST matBound[0] = 1;// .25; matBound[1] = 3.5;// 10; //Up to 6Y maturities strikeBound[0] = 0.5;// 0.5; strikeBound[1] = 2;//1.5; */ HestonCallOptimizationProblem problem = NewOptimizationProblem(equityCalData, matBound, strikeBound); int totalOpts = problem.numCall + problem.numPut; Console.WriteLine("Calibration based on "+totalOpts+ " options. (" + problem.numCall + " call options and "+problem.numPut+" put options)."); IOptimizationAlgorithm solver = new QADE(); //IOptimizationAlgorithm solver = new MultiLevelSingleLinkage(); IOptimizationAlgorithm solver2 = new SteepestDescent(); DESettings o = new DESettings(); o.controller = controller; // If true the optimization algorithm will operate in parallel. o.Parallel = Engine.MultiThread; o.h = 10e-8; o.epsilon = 10e-8; SolutionInfo solution = null; double minObj=double.MaxValue; Vector minX= null; int Z = 1; //if (problem.GetType() == typeof(Heston.HestonCallSimulationOptimizationProblem)) // Z = 2; for(int z=0;z<Z;z++) { if (solver.GetType() == typeof(MultiLevelSingleLinkage)) { o.NP = 50; o.MaxIter = 25; o.MaxGamma = 6; } else { o.NP = 60; o.MaxIter = 35; } o.Verbosity = 1; Vector x0 = null;// new Vector(new double[] { 0.5, 0.5, 0.8, -0.5, 0.05 }); // GA solution = solver.Minimize(problem, o, x0); if (solution.errors) return null; o.options = "qn"; o.MaxIter = 500;// 1000; if (solution != null) solution = solver2.Minimize(problem, o, solution.x); else { solution = solver2.Minimize(problem, o, x0); } if (solution.errors) return null; if (solution.obj < minObj) { minObj = solution.obj; minX = solution.x.Clone(); } } solution.obj = minObj; solution.x = minX; //Displays pricing error structure HestonCallOptimizationProblem.displayObjInfo = true; problem.Obj(solution.x); HestonCallOptimizationProblem.displayObjInfo = false; Console.WriteLine("Calibration Time (s)\t" + (DateTime.Now - t0).TotalSeconds); return BuildEstimate(spotPrice,interestDataSet, callDataSet, equityCalData, solution); }
protected virtual HestonCallOptimizationProblem NewOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound) { return new HestonCallOptimizationProblem(equityCalData, matBound, strikeBound); }
protected virtual EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution) { string[] names = new string[] { "S0", "kappa", "theta", "sigma", "rho", "V0" }; Vector param = new Vector(6); param[0] = spotPrice.Value; param[Range.New(1, 5)] = solution.x; var result = new EstimationResult(names, param); // In the following the two function describing the ZR and dividend yields are created //Matrix zerorate = new Matrix(interestDataSet.Durations.Length, 2); //zerorate[Range.All, 0] = interestDataSet.Durations; //zerorate[Range.All, 1] = interestDataSet.Values; //Matrix dividendYield = new Matrix(equityCalData.MaturityDY.Length, 2); //dividendYield[Range.All, 0] = equityCalData.MaturityDY; //dividendYield[Range.All, 1] = equityCalData.DividendYield; Matrix zerorate = new Matrix((equityCalData.zrFunc as PFunction).Expr); //Matrix dividendYield = new Matrix((equityCalData.dyFunc as PFunction).Expr); Matrix dividendYield = ToMatrix(IstantaneousDividendYield(equityCalData)); result.Objects = new object[2]; result.Objects[0] = zerorate; result.Objects[1] = dividendYield; result.Fit = solution.obj; Console.WriteLine(result); return result; }
protected virtual HestonCallOptimizationProblem NewOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound) { return(new HestonCallOptimizationProblem(equityCalData, matBound, strikeBound)); }
/// <summary> /// Attempts to solve the Heston optimization problem using /// <see cref="Heston.HestonOptimizationProblem"/>. /// </summary> /// <param name="marketData">Data to be used in order to perform the optimization.</param> /// <param name="settings">The parameter is not used.</param> /// <param name="controller">IController.</param> /// <returns>The results of the optimization.</returns> public EstimationResult Estimate(List <object> marketData, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null) { DateTime t0 = DateTime.Now; var interestDataSet = (CurveMarketData)marketData[0]; CallPriceMarketData callDataSet = (CallPriceMarketData)marketData[1]; EquityCalibrationData equityCalData = new EquityCalibrationData(callDataSet, interestDataSet); var spotPrice = (DVPLI.MarketDataTypes.Scalar)marketData[2]; Setup(equityCalData, settings); var calSettings = settings as HestonCalibrationSettings; // Creates the context. Document doc = new Document(); ProjectROV prj = new ProjectROV(doc); doc.Part.Add(prj); // Optimization problem instance. Vector matBound = new Vector(2); Vector strikeBound = new Vector(2); if (calSettings != null) { matBound[0] = calSettings.MinMaturity; matBound[1] = calSettings.MaxMaturity; strikeBound[0] = calSettings.MinStrike; strikeBound[1] = calSettings.MaxStrike; } else { //use defaults matBound[0] = 1.0 / 12; // .25; matBound[1] = 6; // 10; //Up to 6Y maturities strikeBound[0] = 0.4; strikeBound[1] = 1.6; } Console.WriteLine(callDataSet); /* * //CBA TEST * matBound[0] = 1;// .25; * matBound[1] = 3.5;// 10; //Up to 6Y maturities * strikeBound[0] = 0.5;// 0.5; * strikeBound[1] = 2;//1.5; */ HestonCallOptimizationProblem problem = NewOptimizationProblem(equityCalData, matBound, strikeBound); int totalOpts = problem.numCall + problem.numPut; Console.WriteLine("Calibration based on " + totalOpts + " options. (" + problem.numCall + " call options and " + problem.numPut + " put options)."); IOptimizationAlgorithm solver = new QADE(); //IOptimizationAlgorithm solver = new MultiLevelSingleLinkage(); IOptimizationAlgorithm solver2 = new SteepestDescent(); DESettings o = new DESettings(); o.controller = controller; // If true the optimization algorithm will operate in parallel. o.Parallel = Engine.MultiThread; o.h = 10e-8; o.epsilon = 10e-8; SolutionInfo solution = null; double minObj = double.MaxValue; Vector minX = null; int Z = 1; //if (problem.GetType() == typeof(Heston.HestonCallSimulationOptimizationProblem)) // Z = 2; for (int z = 0; z < Z; z++) { if (solver.GetType() == typeof(MultiLevelSingleLinkage)) { o.NP = 50; o.MaxIter = 25; o.MaxGamma = 6; } else { o.NP = 60; o.MaxIter = 35; } o.Verbosity = 1; Vector x0 = null;// new Vector(new double[] { 0.5, 0.5, 0.8, -0.5, 0.05 }); // GA solution = solver.Minimize(problem, o, x0); if (solution.errors) { return(null); } o.options = "qn"; o.MaxIter = 500;// 1000; if (solution != null) { solution = solver2.Minimize(problem, o, solution.x); } else { solution = solver2.Minimize(problem, o, x0); } if (solution.errors) { return(null); } if (solution.obj < minObj) { minObj = solution.obj; minX = solution.x.Clone(); } } solution.obj = minObj; solution.x = minX; //Displays pricing error structure HestonCallOptimizationProblem.displayObjInfo = true; problem.Obj(solution.x); HestonCallOptimizationProblem.displayObjInfo = false; Console.WriteLine("Calibration Time (s)\t" + (DateTime.Now - t0).TotalSeconds); return(BuildEstimate(spotPrice, interestDataSet, callDataSet, equityCalData, solution)); }
protected override HestonCallOptimizationProblem NewOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound) { return(new HestonCallSimulationOptimizationProblem(equityCalData, matBound, strikeBound)); }
protected override void Setup(EquityCalibrationData equityCalData, IEstimationSettings settings) { //No need to used constant values. In the optimization procedure we can use the term structure //as it is. /* //equityCalData.dyFunc= LeastSquaresDividendCalibration(equityCalData.Hdata, equityCalData.zrFunc); if (settings != null) //uses settings if provided. { var localSettings = (HestonEstimationSettings)settings; equityCalData.SetToSpecificMaturity(localSettings.Maturity); } else equityCalData.SetToSpecificMaturity(1); */ DY(equityCalData); return; }
private EstimationResult QuantLibEstimate(CurveMarketData discoutingCurve, CallPriceMarketData Hdataset) { EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discoutingCurve); bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2); if (hasArbitrage) { Console.WriteLine("Market data contains arbitrage opportunity"); } this.r = new DVPLDOM.PFunction(discoutingCurve.Durations, discoutingCurve.Values); this.q = HCalData.dyFunc as PFunction; //this.r.Parse(null); //this.q.Parse(null); Hdataset.Volatility = new Matrix(Hdataset.CallPrice.R, Hdataset.CallPrice.C); for (int i = 0; i < Hdataset.Volatility.R; i++) { double m = Hdataset.Maturity[i]; for (int j = 0; j < Hdataset.Volatility.C; j++) { if (Hdataset.CallPrice[i, j] > 0) { var bs = new Fairmat.Finance.BlackScholes(r.Evaluate(m), Hdataset.S0, Hdataset.Strike[j], 0, m, q.Evaluate(m)); //Hdataset.Volatility[i, j] = Hdataset.Volatility[i, j] * Hdataset.Volatility[i, j] * Hdataset.Maturity[i]; //Hdataset.Volatility[i, j] = bs.ImpliedCallVolatility(Hdataset.CallPrice[i, j]); } } } Console.WriteLine(Hdataset.Volatility); IFunction impVol = FitImplVolModel(Hdataset); Document doc = new Document(); ProjectROV prj = new ProjectROV(doc); doc.Part.Add(prj); prj.Symbols.Add(impVol); // doc.WriteToXMLFile("impVol.fair"); int nmat = calibrationSettings.LocalVolatilityMaturities; int nstrike = calibrationSettings.LocalVolatilityStrikes; double lastMat = Hdataset.Maturity[SymbolicIntervalExtremes.End]; double lastStr = Hdataset.Strike[SymbolicIntervalExtremes.End]; Vector locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat); Vector locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike); Matrix locVolMatrix = new Matrix(nmat, nstrike); double t, dt, forwardValue, y, dy, strike, strikep, strikem, w, wp, wm, dwdy; double d2wdy2, den1, den2, den3, strikept, strikemt, wpt, wmt, dwdt; Integrate integrate = new Integrate(this); for (int i = 0; i < nmat; i++) { t = locVolMat[i]; forwardValue = Hdataset.S0 * Math.Exp(integrate.AdaptLobatto(0.0, t)); for (int j = 0; j < nstrike; j++) { strike = locVolStr[j]; y = Math.Log(strike / forwardValue); dy = ((Math.Abs(y) > 0.001) ? y * 0.0001 : 0.000001); // strike derivative strikep = strike * Math.Exp(dy); strikem = strike / Math.Exp(dy); w = impVol.Evaluate(t, strike); wp = impVol.Evaluate(t, strikep); wm = impVol.Evaluate(t, strikem); dwdy = (wp - wm) / (2.0 * dy); d2wdy2 = (wp - 2.0 * w + wm) / (dy * dy); // time derivative if (t == 0.0) { dt = 0.0001; strikept = strike * Math.Exp(integrate.AdaptLobatto(0.0, t + dt)); wpt = impVol.Evaluate(t + dt, strikept); // if (wpt < w) // Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt); dwdt = (wpt - w) / dt; } else { dt = Math.Min(0.0001, t / 2.0); strikept = strike * Math.Exp(integrate.AdaptLobatto(t, t + dt)); strikemt = strike * Math.Exp(-integrate.AdaptLobatto(t - dt, t)); wpt = impVol.Evaluate(t + dt, strikept); wmt = impVol.Evaluate(t + dt, strikemt); //if (wpt < w) // Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt); //if (w < wmt) // Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t-dt, t); dwdt = (wpt - wmt) / (2.0 * dt); } if (dwdy == 0.0 && d2wdy2 == 0.0) { locVolMatrix[i, j] = Math.Sqrt(dwdt); } else { den1 = 1.0 - y / w * dwdy; den2 = 0.25 * (-0.25 - 1.0 / w + y * y / w / w) * dwdy * dwdy; den3 = 0.5 * d2wdy2; locVolMatrix[i, j] = dwdt / (den1 + den2 + den3); //if (locVolMatrix[i,j] < 0.0) // Console.WriteLine("Negative local vol^2 at strike {0} and time {1}; " + // "Black vol surface is not smooth enought.", strike, t); } } } // Create dupire outputs. Console.WriteLine(locVolMat); PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix); localVol.Parse(null); string[] names = new string[] { "S0" }; Vector param = new Vector(1); param[0] = Hdataset.S0; EstimationResult result = new EstimationResult(names, param); //result.Objects = new object[3]; result.Objects = new object[4]; result.Objects[0] = this.r; result.Objects[1] = this.q; result.Objects[2] = localVol; result.Objects[3] = impVol; //Console.WriteLine("r = " + HCalData.Rate.ToString()); //Console.WriteLine("q = " + HCalData.DividendYield.ToString()); return(result); }
protected override EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution) { string[] names = new string[] { "S0", "kappa", "theta", "sigma", "rho", "V0", "r", "q" }; Vector param = new Vector(8); param[0] = spotPrice.Value; param[Range.New(1, 5)] = solution.x[Range.New(0, 4)]; param[6] = equityCalData.zrFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity); if (impliedDividends) param[7] = solution.x[Range.End];// equityCalData.dyFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity); else param[7] = DY(equityCalData); var result = new EstimationResult(names, param); result.Fit = HestonCallOptimizationProblem.avgPricingError; Console.WriteLine(result); return result; }
private EstimationResult QuantLibEstimate(CurveMarketData discoutingCurve, CallPriceMarketData Hdataset) { EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discoutingCurve); bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2); if (hasArbitrage) Console.WriteLine("Market data contains arbitrage opportunity"); this.r = new DVPLDOM.PFunction(discoutingCurve.Durations,discoutingCurve.Values); this.q = HCalData.dyFunc as PFunction; //this.r.Parse(null); //this.q.Parse(null); Hdataset.Volatility = new Matrix(Hdataset.CallPrice.R, Hdataset.CallPrice.C); for (int i = 0; i < Hdataset.Volatility.R; i++) { double m=Hdataset.Maturity[i]; for (int j = 0; j < Hdataset.Volatility.C; j++) { if (Hdataset.CallPrice[i, j] > 0) { var bs = new Fairmat.Finance.BlackScholes(r.Evaluate(m), Hdataset.S0, Hdataset.Strike[j], 0, m, q.Evaluate(m)); //Hdataset.Volatility[i, j] = Hdataset.Volatility[i, j] * Hdataset.Volatility[i, j] * Hdataset.Maturity[i]; //Hdataset.Volatility[i, j] = bs.ImpliedCallVolatility(Hdataset.CallPrice[i, j]); } } } Console.WriteLine(Hdataset.Volatility); IFunction impVol = FitImplVolModel(Hdataset); Document doc = new Document(); ProjectROV prj = new ProjectROV(doc); doc.Part.Add(prj); prj.Symbols.Add(impVol); // doc.WriteToXMLFile("impVol.fair"); int nmat = calibrationSettings.LocalVolatilityMaturities; int nstrike = calibrationSettings.LocalVolatilityStrikes; double lastMat = Hdataset.Maturity[SymbolicIntervalExtremes.End]; double lastStr = Hdataset.Strike[SymbolicIntervalExtremes.End]; Vector locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat); Vector locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike); Matrix locVolMatrix = new Matrix(nmat, nstrike); double t, dt, forwardValue, y, dy, strike, strikep, strikem, w, wp, wm, dwdy; double d2wdy2, den1, den2, den3, strikept, strikemt, wpt, wmt, dwdt; Integrate integrate = new Integrate(this); for (int i = 0; i < nmat; i++) { t = locVolMat[i]; forwardValue = Hdataset.S0 * Math.Exp(integrate.AdaptLobatto(0.0, t)); for (int j = 0; j < nstrike; j++) { strike = locVolStr[j]; y = Math.Log(strike / forwardValue); dy = ((Math.Abs(y) > 0.001) ? y * 0.0001 : 0.000001); // strike derivative strikep = strike * Math.Exp(dy); strikem = strike / Math.Exp(dy); w = impVol.Evaluate(t, strike); wp = impVol.Evaluate(t, strikep); wm = impVol.Evaluate(t, strikem); dwdy = (wp - wm) / (2.0 * dy); d2wdy2 = (wp - 2.0 * w + wm) / (dy * dy); // time derivative if (t == 0.0) { dt = 0.0001; strikept = strike * Math.Exp(integrate.AdaptLobatto(0.0, t + dt)); wpt = impVol.Evaluate(t + dt, strikept); // if (wpt < w) // Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt); dwdt = (wpt - w) / dt; } else { dt = Math.Min(0.0001, t / 2.0); strikept = strike * Math.Exp(integrate.AdaptLobatto(t, t + dt)); strikemt = strike * Math.Exp(-integrate.AdaptLobatto(t - dt, t)); wpt = impVol.Evaluate(t + dt, strikept); wmt = impVol.Evaluate(t + dt, strikemt); //if (wpt < w) // Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt); //if (w < wmt) // Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t-dt, t); dwdt = (wpt - wmt) / (2.0 * dt); } if (dwdy == 0.0 && d2wdy2 == 0.0) locVolMatrix[i, j] = Math.Sqrt(dwdt); else { den1 = 1.0 - y / w * dwdy; den2 = 0.25 * (-0.25 - 1.0 / w + y * y / w / w) * dwdy * dwdy; den3 = 0.5 * d2wdy2; locVolMatrix[i, j] = dwdt / (den1 + den2 + den3); //if (locVolMatrix[i,j] < 0.0) // Console.WriteLine("Negative local vol^2 at strike {0} and time {1}; " + // "Black vol surface is not smooth enought.", strike, t); } } } // Create dupire outputs. Console.WriteLine(locVolMat); PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix); localVol.Parse(null); string[] names = new string[] { "S0" }; Vector param = new Vector(1); param[0] = Hdataset.S0; EstimationResult result = new EstimationResult(names, param); //result.Objects = new object[3]; result.Objects = new object[4]; result.Objects[0] = this.r; result.Objects[1] = this.q; result.Objects[2] = localVol; result.Objects[3] = impVol; //Console.WriteLine("r = " + HCalData.Rate.ToString()); //Console.WriteLine("q = " + HCalData.DividendYield.ToString()); return result; }