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);
        }
        public void Test()
        {
            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)0.0704877770928728;
            process.sigma1 = (ModelParameter)0.116251516678772;
            process.zr     = (ModelParameter)"@zr";

            StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);

            rov.Processes.AddProcess(s);

            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);
        }
        public void Test()
        {
            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)0.0704877770928728;
            process.sigma1 = (ModelParameter)0.116251516678772;
            process.zr = (ModelParameter)"@zr";

            StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
            rov.Processes.AddProcess(s);

            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);
        }
        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);
        }
Example #5
0
        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);
        }
Example #6
0
        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);
        }
Example #8
0
        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);
        }
Example #9
0
        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);
        }
Example #10
0
        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);
        }
Example #12
0
        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);
        }
Example #13
0
        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);
        }
Example #14
0
        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);
        }
Example #15
0
        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);
        }
Example #16
0
        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);
        }
Example #17
0
        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);
        }
Example #18
0
        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);
        }
Example #21
0
        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);
        }