Exemple #1
0
        // Bisection Algorithm for Black Scholes Implied Volatility =================================================================================
        public double BisectionMSIV(double S, double K, double r, double q, double T, double a, double b, double MktPrice, double Tol, int MaxIter, double B, double dt)
        {
            MSPrices MS        = new MSPrices();
            double   lowPrice  = MS.MSPriceBS(S, K, T, a, r, q, MaxIter, Tol, B, dt);
            double   highPrice = MS.MSPriceBS(S, K, T, b, r, q, MaxIter, Tol, B, dt);
            double   lowCdif   = MktPrice - lowPrice;
            double   highCdif  = MktPrice - highPrice;
            double   y         = 0.0;
            double   midP;

            if (lowCdif * highCdif > 0.0)
            {
                y = -1.0;
            }
            else
            {
                for (int x = 0; x <= MaxIter; x++)
                {
                    midP = (a + b) / 2.0;
                    double midCdif = MktPrice - MS.MSPriceBS(S, K, T, midP, r, q, MaxIter, Tol, B, dt);
                    if (Math.Abs(midCdif) < Tol)
                    {
                        break;
                    }
                    else
                    {
                        if (midCdif > 0.0)
                        {
                            a = midP;
                        }
                        else
                        {
                            b = midP;
                        }
                    }
                    y = midP;
                }
            }
            return(y);
        }
        // Objective function ===========================================================================
        public double f(double[] param, OFSet ofsettings)
        {
            // Option price settings
            double S    = ofsettings.opsettings.S;
            double r    = ofsettings.opsettings.r;
            double q    = ofsettings.opsettings.q;
            double T    = ofsettings.opsettings.T;
            int    trap = ofsettings.opsettings.trap;

            // Market data
            double[] MktIV = ofsettings.data.MktIV;
            int      NK    = MktIV.Length;

            // MS settings
            double dt      = ofsettings.mssettings.dt;
            double a       = ofsettings.mssettings.a;
            double b       = ofsettings.mssettings.b;
            double tol     = ofsettings.mssettings.tol;
            int    MaxIter = ofsettings.mssettings.MaxIter;

            // Optimizatin settings
            double[] lb = ofsettings.lb;
            double[] ub = ofsettings.ub;
            double[] X  = ofsettings.X;
            double[] W  = ofsettings.W;

            HParam param2 = new HParam();

            param2.kappa  = param[0];
            param2.theta  = param[1];
            param2.sigma  = param[2];
            param2.v0     = param[3];
            param2.rho    = param[4];
            param2.lambda = 0.0;

            // Settings for the Bisection algorithm
            a = 0.01;
            b = 3.0;
            double B = 3.0;

            // Initialize the model price and model implied vol vectors, and the objective function value
            double[] ModelPrice = new double[NK];
            double[] ModelIV    = new double[NK];
            double[] Error      = new double[NK];
            double   SumError   = 0.0;

            // Parameter bounds
            double kappaLB = lb[0]; double kappaUB = ub[0];
            double thetaLB = lb[1]; double thetaUB = ub[1];
            double sigmaLB = lb[2]; double sigmaUB = ub[2];
            double v0LB = lb[3]; double v0UB = ub[3];
            double rhoLB = lb[4]; double rhoUB = ub[4];

            // Classes
            MSPrices            MS = new MSPrices();
            BisectionImpliedVol BA = new BisectionImpliedVol();

            // Penalty for inadmissible parameter values
            if ((param2.kappa <= kappaLB) || (param2.theta <= thetaLB) || (param2.sigma <= sigmaLB) || (param2.v0 <= v0LB) || (param2.rho <= rhoLB) ||
                (param2.kappa >= kappaUB) || (param2.theta >= thetaUB) || (param2.sigma >= sigmaUB) || (param2.v0 >= v0UB) || (param2.rho >= rhoUB))
            {
                SumError = 1.0e50;
            }

            // Penalty for inadmissible implied vol
            else
            {
                Console.WriteLine("----------------------------------------");
                Console.WriteLine("ModelPrice ImpliedVol   MktVol    Error");
                Console.WriteLine("----------------------------------------");
                for (int k = 0; k <= NK - 1; k++)
                {
                    double Strike = ofsettings.data.K[k];
                    ofsettings.opsettings.K = Strike;
                    double[] output = new double[6];
                    output        = MS.MSPriceHeston(param2, ofsettings.opsettings, ofsettings.mssettings);
                    ModelPrice[k] = Math.Max(0.01, output[2]);
                    ModelIV[k]    = BA.BisectionMSIV(S, Strike, r, q, T, a, b, ModelPrice[k], tol, MaxIter, B, dt);
                    if (ModelIV[k] == -1.0)
                    {
                        Error[k] = 1.0e50;
                    }
                    else
                    {
                        Error[k] = Math.Pow(ModelIV[k] - MktIV[k], 2.0);
                    }
                    Console.WriteLine("{0,7:F4} {1,10:F4} {2,10:F4} {3,10:F6}", ModelPrice[k], ModelIV[k], MktIV[k], Error[k]);
                    SumError += Error[k];
                }
            }
            return(SumError);
        }
Exemple #3
0
        static void Main(string[] args)
        {
            // 32 point Gauss Laguerre
            double[] X = new Double[32];
            double[] W = new Double[32];
            using (TextReader reader = File.OpenText("../../GaussLaguerre32.txt"))
            {
                for (int k = 0; k <= 31; k++)
                {
                    string   text = reader.ReadLine();
                    string[] bits = text.Split(' ');
                    X[k] = double.Parse(bits[0]);
                    W[k] = double.Parse(bits[1]);
                }
            }

            // Bounds on the parameter estimates
            // kappa theta sigma v0 rho
            double e = 1e-5;

            double[] lb = new double[5] {
                e, e, e, e, -0.99
            };
            double[] ub = new double[5] {
                20.0, 2.0, 5.0, 2.0, 0.99
            };

            //// IBM put prices May 7, 2010
            double S = 122.10;

            //double[,] MktPrice = new double[8,5]{
            //    { 0.130,  0.620,  1.275,  2.950,  4.750},
            //    { 0.260,  0.955,  1.830,  3.925,  6.075},
            //    { 0.485,  1.500,  2.610,  5.200,  7.625},
            //    { 0.995,  2.445,  3.775,  6.800,  9.375},
            //    { 2.155,  3.900,  5.475,  8.800, 11.550},
            //    { 4.525,  6.225,  7.775, 11.225, 13.975},
            //    { 8.375,  9.525, 10.850, 14.125, 16.775},
            //    {13.075, 13.600, 14.575, 17.425, 19.900}};

            // Use the first set of prices, for the first maturity
            double[] MktPrice = new double[8] {
                0.130, 0.260, 0.485, 0.995, 2.155, 4.525, 8.375, 13.075
            };
            double[] K = new double[8] {
                100.0, 105.0, 110.0, 115.0, 120.0, 125.0, 130.0, 135.0
            };
            double r = 0.015;
            double q = 0.01;
            //double[] T = new double[5] {0.0384,0.1151, 0.1918, 0.4411, 0.7096};
            double T  = 0.0384;
            int    NK = 8;

            // Bisection algorithm
            double a       = 0.01;
            double b       = 2.00;
            double Tol     = 1.0e-5;
            int    MaxIter = 1000;
            double B       = 2.0;
            double dt      = 1.0e-10;

            // Implied volatilities
            BisectionImpliedVol BA = new BisectionImpliedVol();

            double[] MktIV = new double[NK];
            for (int k = 0; k <= NK - 1; k++)
            {
                MktIV[k] = BA.BisectionMSIV(S, K[k], r, q, T, a, b, MktPrice[k], Tol, MaxIter, B, dt);
            }

            MktData MktData = new MktData();

            MktData.MktIV   = MktIV;
            MktData.K       = K;
            MktData.PutCall = "P";

            OpSet opsettings = new OpSet();

            opsettings.S       = S;
            opsettings.T       = T;
            opsettings.r       = r;
            opsettings.q       = q;
            opsettings.PutCall = "P";
            opsettings.trap    = 1;

            MSSet mssettings = new MSSet();

            mssettings.method   = 3;
            mssettings.A        = 0.0001;
            mssettings.B        = 100.0;
            mssettings.N        = 3000;
            mssettings.dt       = 1.0e-10;
            mssettings.tol      = 1.0e-5;
            mssettings.MaxIter  = 1000;
            mssettings.NumTerms = 3;
            mssettings.yinf     = 1.0e4;
            mssettings.a        = -10.0;
            mssettings.b        = +10.0;

            OFSet ofsettings = new OFSet();

            ofsettings.opsettings = opsettings;
            ofsettings.mssettings = mssettings;
            ofsettings.data       = MktData;
            ofsettings.X          = X;
            ofsettings.W          = W;
            ofsettings.lb         = lb;
            ofsettings.ub         = ub;

            // Settings for the Nelder Mead algorithm
            NMSet nmsettings;

            nmsettings.N          = 5;               // Number of Heston parameters
            nmsettings.MaxIters   = 20;              // Maximum number of iterations
            nmsettings.Tolerance  = 1e-6;            // Tolerance on best and worst function values
            nmsettings.ofsettings = ofsettings;

            // Starting values (vertices) in vector form.  Add random increment about each starting value
            NelderMeadAlgo NM     = new NelderMeadAlgo();
            double         kappaS = 20.00;
            double         thetaS = 0.036;
            double         sigmaS = 3.9;
            double         v0S    = 0.15;
            double         rhoS   = -0.46;
            int            N      = nmsettings.N;

            double[,] x = new double[N, N + 1];
            for (int j = 0; j <= N; j++)
            {
                x[0, j] = kappaS + NM.RandomNum(-0.01, 0.01) * kappaS;
                x[1, j] = thetaS + NM.RandomNum(-0.01, 0.01) * thetaS;
                x[2, j] = sigmaS + NM.RandomNum(-0.01, 0.01) * sigmaS;
                x[3, j] = v0S + NM.RandomNum(-0.01, 0.01) * v0S;
                x[4, j] = rhoS + NM.RandomNum(-0.01, 0.01) * rhoS;
            }

            // Obtain the parameter estimates
            ObjectiveFunction OF = new ObjectiveFunction();

            double[] BB = NM.NelderMead(OF.f, nmsettings, x);

            HParam paramEst = new HParam();

            paramEst.kappa  = BB[0];
            paramEst.theta  = BB[1];
            paramEst.sigma  = BB[2];
            paramEst.v0     = BB[3];
            paramEst.rho    = BB[4];
            paramEst.lambda = 0.0;

            // Obtain the fitted implied vols
            MSPrices MS = new MSPrices();

            double[] ModelIV    = new double[NK];
            double[] ModelPrice = new double[NK];
            double[] output     = new double[6];
            double   IVMSE      = 0.0;

            for (int k = 0; k <= NK - 1; k++)
            {
                opsettings.K  = K[k];
                output        = MS.MSPriceHeston(paramEst, opsettings, mssettings);
                ModelPrice[k] = output[2];
                ModelIV[k]    = BA.BisectionMSIV(S, K[k], r, q, T, a, b, ModelPrice[k], Tol, MaxIter, B, dt);
                IVMSE        += Math.Pow(ModelIV[k] - MktIV[k], 2.0);
            }

            // Output the estimation result
            Console.WriteLine("  ");
            Console.WriteLine("Parameter Estimates --------------------");
            Console.WriteLine("  ");
            Console.WriteLine("kappa   =  {0:F5}", BB[0]);
            Console.WriteLine("theta   =  {0:F5}", BB[1]);
            Console.WriteLine("sigma   =  {0:F5}", BB[2]);
            Console.WriteLine("v0      =  {0:F5}", BB[3]);
            Console.WriteLine("rho     =  {0:F5}", BB[4]);
            Console.WriteLine("  ");
            Console.WriteLine("Value of the objective function is  {0:E5}", BB[5]);
            Console.WriteLine("Number of iterations required       {0:0}", BB[6]);
            Console.WriteLine("  ");
            Console.WriteLine("----------------------------------------");
            Console.WriteLine(" ");
            Console.WriteLine("Strike    MktIV   ModelIV");
            Console.WriteLine("-------------------------");
            for (int k = 0; k <= NK - 1; k++)
            {
                Console.WriteLine("{0,3:F0} {1,12:F5} {2,12:F5}", K[k], MktIV[k], ModelIV[k]);
            }
        }