public static void Calculate(double t1, double t2, double simEnd, int numSim, int numSteps, out double val, out double stDev) { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)0.05; rov.Symbols.Add(zerorate); // To be changed to 350000. int n_sim = numSim; int n_steps = numSteps; SquaredGaussianModel process = new SquaredGaussianModel(); process.a1 = (ModelParameter)0.1; process.sigma1 = (ModelParameter)0.01; process.zr = (ModelParameter)"@zr"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = 0.0; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "bond(" + t1.ToString() + ";" + t2.ToString() + ";@v1)"; // Here we put the simulation maturity. op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)simEnd; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } ResultItem price = rov.m_ResultList[0] as ResultItem; val = price.value; stDev = price.stdDev / Math.Sqrt((double)numSim); }
private static ProjectROV HullAndWhite1(string payoff, double maturity, double a1, double sigma1) { Document doc = new Document(); ProjectROV rov1 = new ProjectROV(doc); doc.Part.Add(rov1); // Create the zero rate curve double a = 0.08; double b = 0.05; double c = -0.18; string zr = string.Format("{0} - {1}*exp({2}*x1)", a, b, c); AFunction zero_rate = new AFunction(rov1); zero_rate.VarName = "ZeroRate"; zero_rate.m_IndependentVariables = 1; zero_rate.m_Value = new RightValueExpression(zr); // Add to the project the created zero rate curve. rov1.Symbols.Add(zero_rate); RiskFreeInfo rfi = rov1.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.ZeroCoupond; rfi.m_deterministicRF.m_Value = (RightValue)"exp( -ZeroRate(t)*t)"; // Create the short rate process. HW1 hw1 = new HW1(a1, sigma1, "@ZeroRate"); StochasticProcessExtendible hw = new StochasticProcessExtendible(rov1, hw1); rov1.Processes.AddProcess(hw); OptionTree ot = new OptionTree(rov1); ot.European = true; ot.PayoffInfo.PayoffExpression = payoff; ot.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity; rov1.Map.Root = ot; return(rov1); }
private static ProjectROV HullAndWhite1(string payoff, double maturity, double a1, double sigma1) { Document doc = new Document(); ProjectROV rov1 = new ProjectROV(doc); doc.Part.Add(rov1); // Create the zero rate curve double a = 0.08; double b = 0.05; double c = -0.18; string zr = string.Format("{0} - {1}*exp({2}*x1)", a, b, c); AFunction zero_rate = new AFunction(rov1); zero_rate.VarName = "ZeroRate"; zero_rate.m_IndependentVariables = 1; zero_rate.m_Value = new RightValueExpression(zr); // Add to the project the created zero rate curve. rov1.Symbols.Add(zero_rate); RiskFreeInfo rfi = rov1.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.ZeroCoupond; rfi.m_deterministicRF.m_Value = (RightValue)"exp( -ZeroRate(t)*t)"; // Create the short rate process. HW1 hw1 = new HW1(a1, sigma1, "@ZeroRate"); StochasticProcessExtendible hw = new StochasticProcessExtendible(rov1, hw1); rov1.Processes.AddProcess(hw); OptionTree ot = new OptionTree(rov1); ot.European = true; ot.PayoffInfo.PayoffExpression = payoff; ot.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity; rov1.Map.Root = ot; return rov1; }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 20000; int n_steps = 1024; double a = 0.2; double DR = 0.02; double r0 = 0.015; double a1 = 0.02; double sigma1 = 0.01; double maturityOpt = 5.0; double strike = 0.005; double tau = 0.5; double strike2 = 1.0 / (1.0 + strike * tau); ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pa = new ModelParameter(a, "a"); Pa.VarName = "a"; rov.Symbols.Add(Pa); ModelParameter PDR = new ModelParameter(DR, "PDR"); PDR.VarName = "DR"; rov.Symbols.Add(PDR); ModelParameter Pr0 = new ModelParameter(r0, "r0"); Pr0.VarName = "r0"; rov.Symbols.Add(Pr0); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0"); rov.Symbols.Add(zerorate); HW1 process = new HW1(a1, sigma1, "@zr"); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@V1"; OptionTree op = new OptionTree(rov); // 1) RATE FUNCTION, with this the price is higher than the theoretical one // op.PayoffInfo.PayoffExpression = "tau*max(rate(TT;tau;@v1) - strike; 0)"; // 2) OBTAIN RATE FROM bond = exp(-rate*t), // with this the price is higher than the theoretical one but it's more near than 1) // op.PayoffInfo.PayoffExpression = "tau*max(-ln(bond(TT;TT+tau;@v1))/tau - strike; 0)"; // 3) CONVERT RATE from discrete to continuous through (1+r_d) = exp(r_c) // In this way the price is the same as the theoretical one. op.PayoffInfo.PayoffExpression = "tau*max(ln(1+rate(TT;tau;@v1)) - strike; 0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt(2.0 * (double)n_sim); // Calculation of the theoretical value of the caplet. CapHW1 cap = new CapHW1(zerorate); double theoreticalPrice = cap.HWCaplet(a1, sigma1, maturityOpt, maturityOpt + tau, strike2); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { // Tests HW1 dynamics comparing the price of a call option on a bond // calculated through simulation and the theoretical one. Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 20000; int n_steps = 1024; double a = 0.2; double DR = 0.02; double r0 = 0.015; double a1 = 0.02; double sigma1 = 0.01; double maturityOpt = 5.0; double strike = 0.98192; double tau = 1.0; ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pa = new ModelParameter(a, "a"); Pa.VarName = "a"; rov.Symbols.Add(Pa); ModelParameter PDR = new ModelParameter(DR, "PDR"); PDR.VarName = "DR"; rov.Symbols.Add(PDR); ModelParameter Pr0 = new ModelParameter(r0, "r0"); Pr0.VarName = "r0"; rov.Symbols.Add(Pr0); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0"); rov.Symbols.Add(zerorate); HW1 process = new HW1(a1, sigma1, "@zr"); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@V1"; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "Max(bond(TT;TT+tau;@v1)-strike;0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); // Calculation of the theoretical value of the call. CapHW1 cap = new CapHW1(zerorate); double d1 = cap.D1(a1, sigma1, maturityOpt, maturityOpt + tau, strike); double d2 = cap.D2(a1, sigma1, maturityOpt, maturityOpt + tau, strike); double theoreticalPrice = ZCB(zerorate, maturityOpt + tau) * SpecialFunctions.NormCdf(d1) - strike * ZCB(zerorate, maturityOpt) * SpecialFunctions.NormCdf(d2); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)0.05; rov.Symbols.Add(zerorate); int n_sim = 4000; double maturityOpt = 6.5; // Simulation steps for a year. With stepPerYear = 150 the test will be passed. // But notice that the price calculated through Monte Carlo is unstable when // changing this value, even till 1000 steps per year. int stepsPerYear = 150; int n_steps = stepsPerYear * ((int)maturityOpt); double strike = 0.01; double tau = 0.5; SquaredGaussianModel process = new SquaredGaussianModel(); process.a1 = (ModelParameter)0.1; process.sigma1 = (ModelParameter)0.01; process.zr = (ModelParameter)"@zr"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@V1"; // Set the payoff. OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "tau*max(rate(TT;tau;@v1) - strike; 0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)(maturityOpt + tau); op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { rov.DisplayErrors(); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double mcPrice = price.value; double mcDevST = price.stdDev / Math.Sqrt((double)n_sim); Caplet cplt = new Caplet(); Vector Mat, fwd, Rk; Vector capMatV; double delta_k; double capMat; delta_k = 0.5; capMat = maturityOpt + tau; int nmat = 2 * ((int)capMat) + 1; Mat = new Vector(nmat); fwd = new Vector(nmat); Mat[0] = 0; fwd[0] = zerorate.Evaluate(0); for (int k = 1; k < nmat; k++) { Mat[k] = tau * ((double)k); fwd[k] = zerorate.Evaluate(Mat[k]) * Mat[k] - zerorate.Evaluate(Mat[k - 1]) * Mat[k - 1]; } fwd = fwd / tau; Rk = new Vector(1); Rk[0] = strike; capMatV = new Vector(2); capMatV[0] = maturityOpt; capMatV[1] = maturityOpt + tau; Matrix caplet = cplt.PGSMCaplets(process, Mat, fwd, Rk, delta_k, capMatV); double theoreticalPrice = caplet[1, 0] - caplet[0, 0]; Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + mcPrice); Console.WriteLine("Standard Deviation = " + mcDevST); double tol = 4.0 * mcDevST; Assert.Less(Math.Abs(theoreticalPrice - mcPrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)0.05; rov.Symbols.Add(zerorate); int n_sim = 5000; int n_steps = 900; SquaredGaussianModel process = new SquaredGaussianModel(); process.a1 = (ModelParameter)0.1; process.sigma1 = (ModelParameter)0.01; process.zr = (ModelParameter)"@zr"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = 0.0; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "bond(t;10;@v1)"; // Set the simulation maturity. op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)2.0; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; Console.WriteLine("Bond Test Value = " + price.value.ToString()); Assert.LessOrEqual(Math.Abs(0.6702 - price.value), .01); // Try to do some simple tests and check the results. double b0_10 = process.Bond(DynamicParam(0, process), process.CacheDates, 0, 0, 10); Console.WriteLine("Bond(0,10) = " + b0_10); Assert.LessOrEqual(Math.Abs(b0_10 - 0.606513), .001); double b7_10 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 10); Console.WriteLine("Bond(7,10) = " + b7_10); Assert.LessOrEqual(Math.Abs(b7_10 - 0.856374), .001); double b7_30 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 30); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 50000; int n_steps = 512; double strike = 100.0; double tau = 5.0; double rate = 0.1; double dy = 0.07; ModelParameter pStrike = new ModelParameter(strike, "strike"); pStrike.VarName = "strike"; rov.Symbols.Add(pStrike); ModelParameter pRate = new ModelParameter(rate, "rfrate"); pRate.VarName = "rfrate"; rov.Symbols.Add(pRate); AFunction payoff = new AFunction(rov); payoff.VarName = "payoff"; payoff.m_IndependentVariables = 1; payoff.m_Value = (RightValue)("max(x1 - strike ; 0)"); rov.Symbols.Add(payoff); HestonProcess process = new HestonProcess(); process.r = (ModelParameter)rate; process.q = (ModelParameter)dy; process.k = (ModelParameter)2.5; process.theta = (ModelParameter)0.4; process.sigma = (ModelParameter)0.2; process.S0 = (ModelParameter)100.0; process.V0 = (ModelParameter)0.3; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = rate; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "payoff(v1a)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)tau; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); // Calculates the theoretical value of the call. Vector param = new Vector(5); param[0] = process.k.V(); param[1] = process.theta.V(); param[2] = process.sigma.V(); param[3] = 0.0; param[4] = process.V0.V(); HestonCall hestonCall = new HestonCall(); double thPrice = hestonCall.HestonCallPrice(param, process.S0.V(), tau, strike, rate, dy); Console.WriteLine("Theoretical Price = " + thPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(thPrice - samplePrice), tol); }
public void TestSimulation() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 10000; int n_steps = 512; double strike = 90.0; double maturity = 2.0; double rate = 0.1; double dy = 0.05; double volatility = 0.2; double S0 = 100; ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike"); rov.Symbols.Add(Pstrike); ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0"); rov.Symbols.Add(PS0); AFunction payoff = new AFunction(rov); payoff.VarName = "payoff"; payoff.m_IndependentVariables = 1; payoff.m_Value = (RightValue)("max(x1 - strike ; 0)"); rov.Symbols.Add(payoff); AFunction rfunc = new AFunction(rov); rfunc.VarName = "r"; rfunc.m_IndependentVariables = 1; rfunc.m_Value = (RightValue)rate; rov.Symbols.Add(rfunc); AFunction qfunc = new AFunction(rov); qfunc.VarName = "q"; qfunc.m_IndependentVariables = 1; qfunc.m_Value = (RightValue)dy; rov.Symbols.Add(qfunc); AFunction volfunc = new AFunction(rov); volfunc.VarName = "localvol"; volfunc.m_IndependentVariables = 2; volfunc.m_Value = (RightValue)volatility; rov.Symbols.Add(volfunc); DupireProcess process = new DupireProcess(); process.s0 = (ModelParameter)"S0"; process.r = (ModelParameter)"@r"; process.q = (ModelParameter)"@q"; process.localVol = (ModelParameter)"@localvol"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = rate; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "payoff(v1)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { rov.DisplayErrors(); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); // Calculation of the theoretical value of the call. double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)0.05; rov.Symbols.Add(zerorate); int n_sim = 5000; int n_steps = 900; SquaredGaussianModel process = new SquaredGaussianModel(); process.a1 = (ModelParameter)0.1; process.sigma1 = (ModelParameter)0.01; process.zr = (ModelParameter)"@zr"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = 0.0; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "bond(t;10;@v1)"; // Set the simulation maturity. op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)2.0; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; Console.WriteLine("Bond Test Value = " + price.value.ToString()); Assert.LessOrEqual(Math.Abs(0.6702 - price.value), .01); // Try to do some simple tests and check the results. double b0_10 = process.Bond(DynamicParam(0, process), process.CacheDates, 0, 0, 10); Console.WriteLine("Bond(0,10) = " + b0_10); Assert.LessOrEqual(Math.Abs(b0_10 - 0.606513), .001); double b7_10 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 10); Console.WriteLine("Bond(7,10) = " + b7_10); Assert.LessOrEqual(Math.Abs(b7_10 - 0.856374), .001); double b7_30 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 30); }
public void Test() { double nu = 0.6; double theta = -0.2; double sigma = 0.2; double rate = 0.02; double dy = 0.01; double s0 = 1; double maturity = 2.0; double strike = 1.2; Vector mat = new Vector(1) + maturity; Vector k = new Vector(1) + strike; // Calculates the theoretical value of the call. double theoreticalPrice = VarianceGammaOptionsCalibration.VGCall(theta, sigma, nu, maturity, strike, dy, s0, rate); Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 50000; int n_steps = 512; ModelParameter paramStrike = new ModelParameter(strike, "strike"); paramStrike.VarName = "strike"; rov.Symbols.Add(paramStrike); ModelParameter paramRate = new ModelParameter(rate, "rfrate"); paramRate.VarName = "rfrate"; rov.Symbols.Add(paramRate); AFunction payoff = new AFunction(rov); payoff.VarName = "payoff"; payoff.m_IndependentVariables = 1; payoff.m_Value = (RightValue)("max(x1 - strike ; 0)"); rov.Symbols.Add(payoff); VarianceGamma process = new VarianceGamma(s0, theta, sigma, nu, rate, dy); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = rate; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "payoff(v1)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { rov.DisplayErrors(); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); Console.WriteLine("Theoretical Price = " + theoreticalPrice); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { // Tests HW1 dynamics comparing the price of a call option on a bond // calculated through simulation and the theoretical one. Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 20000; int n_steps = 1024; double a = 0.2; double DR = 0.02; double r0 = 0.015; double a1 = 0.02; double sigma1 = 0.01; double maturityOpt = 5.0; double strike = 0.98192; double tau = 1.0; ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pa = new ModelParameter(a, "a"); Pa.VarName = "a"; rov.Symbols.Add(Pa); ModelParameter PDR = new ModelParameter(DR, "PDR"); PDR.VarName = "DR"; rov.Symbols.Add(PDR); ModelParameter Pr0 = new ModelParameter(r0, "r0"); Pr0.VarName = "r0"; rov.Symbols.Add(Pr0); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0"); rov.Symbols.Add(zerorate); HW1 process = new HW1(a1, sigma1, "@zr"); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@V1"; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "Max(bond(TT;TT+tau;@v1)-strike;0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); // Calculation of the theoretical value of the call. CapHW1 cap = new CapHW1(zerorate); double d1 = cap.D1(a1, sigma1, maturityOpt, maturityOpt + tau, strike); double d2 = cap.D2(a1, sigma1, maturityOpt, maturityOpt + tau, strike); double theoreticalPrice = ZCB(zerorate, maturityOpt + tau) * SpecialFunctions.NormCdf(d1) - strike * ZCB(zerorate, maturityOpt) * SpecialFunctions.NormCdf(d2); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 20000; int n_steps = 1024; double a = 0.2; double DR = 0.02; double r0 = 0.015; double a1 = 0.02; double sigma1 = 0.01; double maturityOpt = 5.0; double strike = 0.005; double tau = 0.5; double strike2 = 1.0 / (1.0 + strike * tau); ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pa = new ModelParameter(a, "a"); Pa.VarName = "a"; rov.Symbols.Add(Pa); ModelParameter PDR = new ModelParameter(DR, "PDR"); PDR.VarName = "DR"; rov.Symbols.Add(PDR); ModelParameter Pr0 = new ModelParameter(r0, "r0"); Pr0.VarName = "r0"; rov.Symbols.Add(Pr0); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0"); rov.Symbols.Add(zerorate); HW1 process = new HW1(a1, sigma1, "@zr"); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@V1"; OptionTree op = new OptionTree(rov); // 1) RATE FUNCTION, with this the price is higher than the theoretical one // op.PayoffInfo.PayoffExpression = "tau*max(rate(TT;tau;@v1) - strike; 0)"; // 2) OBTAIN RATE FROM bond = exp(-rate*t), // with this the price is higher than the theoretical one but it's more near than 1) // op.PayoffInfo.PayoffExpression = "tau*max(-ln(bond(TT;TT+tau;@v1))/tau - strike; 0)"; // 3) CONVERT RATE from discrete to continuous through (1+r_d) = exp(r_c) // In this way the price is the same as the theoretical one. op.PayoffInfo.PayoffExpression = "tau*max(ln(1+rate(TT;tau;@v1)) - strike; 0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt(2.0 * (double)n_sim); // Calculation of the theoretical value of the caplet. CapHW1 cap = new CapHW1(zerorate); double theoreticalPrice = cap.HWCaplet(a1, sigma1, maturityOpt, maturityOpt + tau, strike2); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 10000; int n_steps = 512; double a = 0.2; double DR = 0.02; double r0 = 0.015; double a1 = 1.0; double sigma1 = 0.01; double a2 = 0.1; double sigma2 = 0.0165; double correlation = 0.6; double maturityOpt = 5.0; double strike = 0.927; double tau = 2.0; ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pa = new ModelParameter(a, "a"); Pa.VarName = "a"; rov.Symbols.Add(Pa); ModelParameter PDR = new ModelParameter(DR, "PDR"); PDR.VarName = "DR"; rov.Symbols.Add(PDR); ModelParameter Pr0 = new ModelParameter(r0, "r0"); Pr0.VarName = "r0"; rov.Symbols.Add(Pr0); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0"); rov.Symbols.Add(zerorate); HW2ProcessType pt = new HW2ProcessType(); // Set the short rate process. pt = HW2ProcessType.ShortRate; StocasticProcessHW2 process1 = new StocasticProcessHW2(rov, pt); process1.zero_rate_curve = "@zr"; process1._a = (ModelParameter)a1; process1._b = (ModelParameter)sigma1; rov.Processes.AddProcess(process1); // Set the mean reversion process. pt = HW2ProcessType.Unobservable; StocasticProcessHW2 process2 = new StocasticProcessHW2(rov, pt); process2._a = (ModelParameter)a2; process2._b = (ModelParameter)sigma2; rov.Processes.AddProcess(process2); // Set the correlation. rov.Processes.r[0, 1] = (RightValue)correlation; // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@v1"; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "max(bond(TT;TT+tau;@v1)-strike;0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double sampleMean = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); double theoreticalPrice = HW2BondCall(zerorate, maturityOpt, maturityOpt + tau, strike, a1, sigma1, a2, sigma2, correlation); Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + sampleMean.ToString()); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); bool result; double fact = 4.0; result = (Math.Abs(sampleMean - theoreticalPrice) < fact * sampleDevSt); Assert.IsTrue(result); }
public void Test() { double nu = 0.6; double theta = -0.2; double sigma = 0.2; double rate = 0.02; double dy = 0.01; double s0 = 1; double maturity = 2.0; double strike = 1.2; Vector mat = new Vector(1) + maturity; Vector k = new Vector(1) + strike; // Calculates the theoretical value of the call. double theoreticalPrice = VarianceGammaOptionsCalibration.VGCall(theta, sigma, nu, maturity, strike, dy, s0, rate); Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 50000; int n_steps = 512; ModelParameter paramStrike = new ModelParameter(strike, "strike"); paramStrike.VarName = "strike"; rov.Symbols.Add(paramStrike); ModelParameter paramRate = new ModelParameter(rate, "rfrate"); paramRate.VarName = "rfrate"; rov.Symbols.Add(paramRate); AFunction payoff = new AFunction(rov); payoff.VarName = "payoff"; payoff.m_IndependentVariables = 1; payoff.m_Value = (RightValue)("max(x1 - strike ; 0)"); rov.Symbols.Add(payoff); VarianceGamma process = new VarianceGamma(s0, theta, sigma, nu, rate, dy); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = rate; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "payoff(v1)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { rov.DisplayErrors(); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); Console.WriteLine("Theoretical Price = " + theoreticalPrice); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 10000; int n_steps = 512; double a = 0.2; double DR = 0.02; double r0 = 0.015; double a1 = 1.0; double sigma1 = 0.01; double a2 = 0.1; double sigma2 = 0.0165; double correlation = 0.6; double maturityOpt = 5.0; double strike = 0.927; double tau = 2.0; ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pa = new ModelParameter(a, "a"); Pa.VarName = "a"; rov.Symbols.Add(Pa); ModelParameter PDR = new ModelParameter(DR, "PDR"); PDR.VarName = "DR"; rov.Symbols.Add(PDR); ModelParameter Pr0 = new ModelParameter(r0, "r0"); Pr0.VarName = "r0"; rov.Symbols.Add(Pr0); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0"); rov.Symbols.Add(zerorate); HW2ProcessType pt = new HW2ProcessType(); // Set the short rate process. pt = HW2ProcessType.ShortRate; StocasticProcessHW2 process1 = new StocasticProcessHW2(rov, pt); process1.zero_rate_curve = "@zr"; process1._a = (ModelParameter)a1; process1._b = (ModelParameter)sigma1; rov.Processes.AddProcess(process1); // Set the mean reversion process. pt = HW2ProcessType.Unobservable; StocasticProcessHW2 process2 = new StocasticProcessHW2(rov, pt); process2._a = (ModelParameter)a2; process2._b = (ModelParameter)sigma2; rov.Processes.AddProcess(process2); // Set the correlation. rov.Processes.r[0, 1] = (RightValue)correlation; // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@v1"; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "max(bond(TT;TT+tau;@v1)-strike;0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double sampleMean = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); double theoreticalPrice = HW2BondCall(zerorate, maturityOpt, maturityOpt + tau, strike, a1, sigma1, a2, sigma2, correlation); Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + sampleMean.ToString()); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); bool result; double fact = 4.0; result = (Math.Abs(sampleMean - theoreticalPrice) < fact * sampleDevSt); Assert.IsTrue(result); }
public void TestSimulation() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 10000; int n_steps = 512; double strike = 90.0; double maturity = 2.0; double rate = 0.1; double dy = 0.05; double volatility = 0.2; double S0 = 100; ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike"); rov.Symbols.Add(Pstrike); ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0"); rov.Symbols.Add(PS0); AFunction payoff = new AFunction(rov); payoff.VarName = "payoff"; payoff.m_IndependentVariables = 1; payoff.m_Value = (RightValue)("max(x1 - strike ; 0)"); rov.Symbols.Add(payoff); AFunction rfunc = new AFunction(rov); rfunc.VarName = "r"; rfunc.m_IndependentVariables = 1; rfunc.m_Value = (RightValue)rate; rov.Symbols.Add(rfunc); AFunction qfunc = new AFunction(rov); qfunc.VarName = "q"; qfunc.m_IndependentVariables = 1; qfunc.m_Value = (RightValue)dy; rov.Symbols.Add(qfunc); AFunction volfunc = new AFunction(rov); volfunc.VarName = "localvol"; volfunc.m_IndependentVariables = 2; volfunc.m_Value = (RightValue)volatility; rov.Symbols.Add(volfunc); DupireProcess process = new DupireProcess(); process.s0 = (ModelParameter)"S0"; process.r = (ModelParameter)"@r"; process.q = (ModelParameter)"@q"; process.localVol = (ModelParameter)"@localvol"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = rate; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "payoff(v1)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { rov.DisplayErrors(); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); // Calculation of the theoretical value of the call. double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 100000; int n_steps = 256; double strike = 90.0; double tau = 2.0; double rate = 0.1; double dy = 0.07; ModelParameter pStrike = new ModelParameter(strike, "strike"); pStrike.VarName = "strike"; rov.Symbols.Add(pStrike); AFunction payoff = new AFunction(rov); payoff.VarName = "payoff"; payoff.m_IndependentVariables = 1; payoff.m_Value = (RightValue)("max(x1 - strike ; 0)"); rov.Symbols.Add(payoff); AFunction zrfunc = new AFunction(rov); zrfunc.VarName = "zr"; zrfunc.m_IndependentVariables = 1; zrfunc.m_Value = (RightValue)rate; rov.Symbols.Add(zrfunc); AFunction dyfunc = new AFunction(rov); dyfunc.VarName = "dy"; dyfunc.m_IndependentVariables = 1; dyfunc.m_Value = (RightValue)dy; rov.Symbols.Add(dyfunc); HestonExtendedProcess process = new HestonExtendedProcess(); process.k = (ModelParameter)2.5; process.theta = (ModelParameter)0.4; process.sigma = (ModelParameter)0.2; process.S0 = (ModelParameter)100.0; process.V0 = (ModelParameter)0.3; process.zrReference = (ModelParameter)"@zr"; process.dyReference = (ModelParameter)"@dy"; double discount = Math.Exp(-rate * tau); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = 0.0; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "payoff(v1a)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)tau; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = discount * price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); // Calculates the theoretical value of the call. Vector param = new Vector(5); param[0] = process.k.V(); param[1] = process.theta.V(); param[2] = process.sigma.V(); param[3] = 0.0; param[4] = process.V0.V(); HestonCall hestonCall = new HestonCall(); double theoreticalPrice = hestonCall.HestonCallPrice(param, process.S0.V(), tau, strike, rate, dy); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol); }
public void Test() { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)0.05; rov.Symbols.Add(zerorate); int n_sim = 10000; double maturityOpt = 6.5; // Simulation steps for a year. With stepPerYear = 150 the test will be passed. // But notice that the price calculated through Monte Carlo is unstable when // changing this value, even till 1000 steps per year. int stepsPerYear = 500; int n_steps = stepsPerYear * ((int)maturityOpt); double strike = 100.0; double tau = 0.5; SquaredGaussianModel process = new SquaredGaussianModel(); process.a1 = (ModelParameter)0.1; process.sigma1 = (ModelParameter)0.01; process.zr = (ModelParameter)"@zr"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); ModelParameter PT = new ModelParameter(maturityOpt, "TT"); PT.VarName = "TT"; rov.Symbols.Add(PT); ModelParameter Ptau = new ModelParameter(tau, "tau"); Ptau.VarName = "tau"; rov.Symbols.Add(Ptau); ModelParameter Pstrike = new ModelParameter(strike, "strike"); Pstrike.VarName = "strike"; rov.Symbols.Add(Pstrike); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.Stochastic; rfi.m_deterministicRF = (ModelParameter)"@V1"; // Set the payoff. OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "max(strike - Bond(TT;TT+tau;@v1); 0)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double mcPrice = price.value; double mcDevST = price.stdDev / Math.Sqrt(2.0 * ((double)n_sim)); Caplet cplt = new Caplet(); Vector Mat; Vector fwd; Vector Rk; Vector capMatV; double deltaK; double capMat; deltaK = 0.5; capMat = maturityOpt + tau; int nmat = 2 * ((int)capMat) + 1; Mat = new Vector(nmat); fwd = new Vector(nmat); Mat[0] = 0; fwd[0] = zerorate.Evaluate(0); for (int k = 1; k < nmat; k++) { Mat[k] = tau * ((double)k); fwd[k] = zerorate.Evaluate(Mat[k]) * Mat[k] - zerorate.Evaluate(Mat[k - 1]) * Mat[k - 1]; } fwd = fwd / tau; Rk = new Vector(1); Rk[0] = (1 / strike - 1.0) / tau; capMatV = new Vector(2); capMatV[0] = maturityOpt; capMatV[1] = maturityOpt + tau; Matrix caplet = cplt.PGSMCaplets(process, Mat, fwd, Rk, deltaK, capMatV); Console.WriteLine("rows = " + caplet.R); Console.WriteLine("columns = " + caplet.C); double theoreticalPrice = caplet[1, 0] - caplet[0, 0]; Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + mcPrice); Console.WriteLine("Standard Deviation = " + mcDevST); double tol = 4.0 * mcDevST; Assert.Less(Math.Abs(theoreticalPrice - mcPrice), tol); }
public void TestCalibration() { InterestRateMarketData IData = InterestRateMarketData.FromFile("../../TestData/IRMD-sample.xml"); CallPriceMarketData HData = CallPriceMarketData.FromFile("../../TestData/CallData-sample.xml"); //InterestRateMarketData IData = InterestRateMarketData.FromFile("../../../EquityModels.Tests/TestData/IRMD-EU-30102012-close.xml"); //CallPriceMarketData HData = CallPriceMarketData.FromFile("../../../EquityModels.Tests/TestData/30102012-SX5E_Index-HestonData.xml"); //CallPriceMarketData HData = ObjectSerialization.ReadFromXMLFile("../../../EquityModels.Tests/TestData/FTSE.xml") as CallPriceMarketData; List <object> l = new List <object>(); l.Add(IData.DiscountingCurve); l.Add(HData); DupireEstimator DE = new DupireEstimator(); DupireCalibrationSettings settings = new DupireCalibrationSettings(); settings.LocalVolatilityCalculation = LocalVolatilityCalculation.Method1; //settings.LocalVolatilityCalculation = LocalVolatilityCalculation.QuantLib; EstimationResult res = DE.Estimate(l, settings); //int nmat = HData.Maturity.Length; //int nstrike = HData.Strike.Length; int i = 5; // Maturity. int j = 4; // Strike. Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); doc.DefaultProject.NMethods.m_UseAntiteticPaths = true; int n_sim = 10000; int n_steps = 500; double strike = HData.Strike[j]; //double volatility = HData.Volatility[i, j]; /* * PFunction2D.PFunction2D impvolfunc = new PFunction2D.PFunction2D(rov); * impvolfunc = res.Objects[3] as PFunction2D.PFunction2D; * impvolfunc.VarName = "impvol"; * rov.Symbols.Add(impvolfunc); * double volatility = impvolfunc.Evaluate(HData.Maturity[i], HData.Strike[j]); */ double volatility = 0.2; double maturity = HData.Maturity[i]; ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike"); rov.Symbols.Add(Pstrike); AFunction payoff = new AFunction(rov); payoff.VarName = "payoff"; payoff.m_IndependentVariables = 1; payoff.m_Value = (RightValue)("max(x1 - strike ; 0)"); rov.Symbols.Add(payoff); bool found; double S0 = PopulateHelper.GetValue("S0", res.Names, res.Values, out found); ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0"); rov.Symbols.Add(PS0); PFunction rfunc = new PFunction(rov); rfunc = res.Objects[0] as PFunction; rfunc.VarName = "r"; rov.Symbols.Add(rfunc); PFunction qfunc = new PFunction(rov); qfunc = res.Objects[1] as PFunction; qfunc.VarName = "q"; rov.Symbols.Add(qfunc); PFunction2D.PFunction2D volfunc = new PFunction2D.PFunction2D(rov); volfunc = res.Objects[2] as PFunction2D.PFunction2D; volfunc.VarName = "localvol"; rov.Symbols.Add(volfunc); DupireProcess process = new DupireProcess(); process.s0 = (ModelParameter)"S0"; process.r = (ModelParameter)"@r"; process.q = (ModelParameter)"@q"; process.localVol = (ModelParameter)"@localvol"; double rate = rfunc.Evaluate(maturity); double dy = qfunc.Evaluate(maturity); StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = rate; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "payoff(v1)"; op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { rov.DisplayErrors(); } Assert.IsFalse(rov.HasErrors); ResultItem price = rov.m_ResultList[0] as ResultItem; double samplePrice = price.value; double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim); Console.WriteLine("Surf = " + volfunc.Expr); // Calculation of the theoretical value of the call. double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy); Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString()); Console.WriteLine("Monte Carlo Price = " + samplePrice); Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString()); double tol = 4.0 * sampleDevSt; doc.WriteToXMLFile("Dupire.fair"); Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), tol); }
public static void Calculate(double t1, double t2, double simEnd, int numSim, int numSteps, out double val, out double stDev) { Engine.MultiThread = true; Document doc = new Document(); ProjectROV rov = new ProjectROV(doc); doc.Part.Add(rov); AFunction zerorate = new AFunction(rov); zerorate.VarName = "zr"; zerorate.m_IndependentVariables = 1; zerorate.m_Value = (RightValue)0.05; rov.Symbols.Add(zerorate); // To be changed to 350000. int n_sim = numSim; int n_steps = numSteps; SquaredGaussianModel process = new SquaredGaussianModel(); process.a1 = (ModelParameter)0.1; process.sigma1 = (ModelParameter)0.01; process.zr = (ModelParameter)"@zr"; StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process); rov.Processes.AddProcess(s); // Set the discounting. RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo; rfi.ActualizationType = EActualizationType.RiskFree; rfi.m_deterministicRF = 0.0; OptionTree op = new OptionTree(rov); op.PayoffInfo.PayoffExpression = "bond(" + t1.ToString() + ";" + t2.ToString() + ";@v1)"; // Here we put the simulation maturity. op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)simEnd; op.PayoffInfo.European = true; rov.Map.Root = op; rov.NMethods.Technology = ETechType.T_SIMULATION; rov.NMethods.PathsNumber = n_sim; rov.NMethods.SimulationSteps = n_steps; ROVSolver solver = new ROVSolver(); solver.BindToProject(rov); solver.DoValuation(-1); if (rov.HasErrors) { Console.WriteLine(rov.m_RuntimeErrorList[0]); } ResultItem price = rov.m_ResultList[0] as ResultItem; val = price.value; stDev = price.stdDev / Math.Sqrt((double)numSim); }