HullAndWhiteOneFactor.CapHW1.D2 C# (CSharp) Method

        public double D2(double a, double sigma, double T, double s, double K)
        {
            return D1(a, sigma, T, s, K) - SigP(a, sigma, T, s);
        }

        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);
        }