Exemplo n.º 1
0
        public double PriceVIXOption(VIXOption Option, Func <double, double> epsilon, double stock_0)
        {
            int    n    = 500;
            double T    = Option.maturity;
            Grid   grid = new Grid(0, T, (int)Math.Abs(T * n));
            int    n_T  = grid.get_timeNmbrStep();

            int kappa = 2;
            //Correlation :
            SymmetricMatrix correl         = MakeCorrel(n, grid);
            SquareMatrix    choleskyCorrel = correl.CholeskyDecomposition().SquareRootMatrix();

            double rho = 0.1;//correlation between the two Brownian
            Func <double, double> payoff;

            switch (Option.type)
            {
            case VIXOption.OptionType.Call:
                payoff = S => Math.Max(S - Option.strike, 0);
                break;

            case VIXOption.OptionType.Put:
                payoff = S => Math.Max(Option.strike - S, 0);
                break;

            default:
                payoff = S => Math.Max(S - Option.strike, 0);
                break;
            }

            double price          = 0.0;
            double McNbSimulation = 1E5;

            for (int mc = 1; mc <= McNbSimulation; mc++)
            {
                // 1-simulation of volterra Hybrid Scheme
                ColumnVector Z;
                ColumnVector volterra;
                //ColumnVector Z_Brownian;

                HybridScheme hybridscheme = new HybridScheme(choleskyCorrel, grid, kappa, H);
                hybridscheme.simulate(out Z, out volterra);

                GaussianSimulator simulator = new GaussianSimulator();
                //Z_Brownian = ExtractBrownian(kappa, n_T, Z, volterra);

                ColumnVector Variance = new ColumnVector(n_T + 1);
                Variance[0] = epsilon(grid.t(0));
                for (int i = 1; i <= grid.get_timeNmbrStep(); i++)
                {
                    Variance[i] = epsilon(grid.t(i)) * Math.Exp(2 * vi * Ch * volterra[i - 1] - Math.Pow(vi * Ch, 2) * Math.Pow(grid.t(i), 2 * H));
                }
                double X = Math.Log(stock_0);
                for (int i = 0; i < n_T; i++)
                {
                    double dW = (rho * Z[i] + Math.Sqrt(1 - Math.Pow(rho, 2)) * Math.Sqrt(grid.get_Step()) * simulator.Next());
                    X = X - 0.5 * Variance[i] * grid.get_Step() + Math.Sqrt(Variance[i]) * dW;
                }

                double S = Math.Exp(X);
                price += payoff(S);
            }
            price /= McNbSimulation;
            return(price);
        }
Exemplo n.º 2
0
        public double VIXfuture_TruncatedChlsky(double T, Func <double, double> epsilon)
        {
            DateTime start = DateTime.Now;
            //StreamWriter sw = new StreamWriter("C:\\Users\\Marouane\\Desktop\\M2IF\\rough volatility\\rBergomiFile.txt");
            //Grid
            int  N    = 100;
            int  S    = 7;
            Grid grid = new Grid(T, T + Delta, N);

            #region  Correlation "Correl Matrix Construction"
            // Small Covariance Matrix t_0 , ... , t_7
            SymmetricMatrix covM_Small = new SymmetricMatrix(S);
            //the full Covariance Matrix
            SymmetricMatrix covM = new SymmetricMatrix(N + 1);
            //Setting for integrale approximations
            EvaluationSettings settings = new EvaluationSettings();
            settings.AbsolutePrecision = 1.0E-7;
            settings.RelativePrecision = 0.0;

            // Small Covariance Calcul t_0,.....,t_7
            for (int i = 0; i < S; i++)
            {
                covM_Small[i, i] = (Math.Pow(grid.t(i), 2 * H) - Math.Pow(grid.t(i) - T, 2 * H)) / (2 * H);
                for (int j = 0; j < i; j++)
                {
                    Func <double, double> covfunc     = t => Math.Pow((grid.t(j) - t) * (grid.t(i) - t), H - 0.5);
                    IntegrationResult     integresult = FunctionMath.Integrate(covfunc, Meta.Numerics.Interval.FromEndpoints(0.0, T), settings);
                    covM_Small[i, j] = integresult.Value;
                }
            }
            // full COrrelation Calcul
            for (int i = 0; i <= N; i++)
            {
                covM[i, i] = (Math.Pow(grid.t(i), 2 * H) - Math.Pow(grid.t(i) - T, 2 * H)) / (2 * H);
                for (int j = 0; j < i; j++)
                {
                    Func <double, double> covfunc     = t => Math.Pow((grid.t(j) - t) * (grid.t(i) - t), H - 0.5);
                    IntegrationResult     integresult = FunctionMath.Integrate(covfunc, Meta.Numerics.Interval.FromEndpoints(0.0, T), settings);
                    covM[i, j] = integresult.Value;
                }
            }

            Func <int, int, double> corrf_Small  = (i, j) => covM_Small[i, j] / (Math.Sqrt(covM_Small[i, i] * covM_Small[j, j]));
            SymmetricMatrix         Correl_Small = new SymmetricMatrix(S);
            Correl_Small.Fill(corrf_Small);

            Func <int, int, double> corrf  = (i, j) => covM[i, j] / (Math.Sqrt(covM[i, i] * covM[j, j]));
            SymmetricMatrix         Correl = new SymmetricMatrix(N + 1);
            Correl.Fill(corrf);
            #endregion

            CholeskyDecomposition cholesky             = Correl_Small.CholeskyDecomposition();
            SquareMatrix          choleskyCorrel_Small = new SquareMatrix(S);
            choleskyCorrel_Small = cholesky.SquareRootMatrix();

            GaussianSimulator simulator = new GaussianSimulator();
            double            VIX       = 0.0;
            var MC = 1.0E5;
            for (int mc = 1; mc < MC; mc++)
            {
                ColumnVector GaussianVector = new ColumnVector(S);
                // Simulating Volterra at 8 first steps on [T, T+Delta]
                for (int i = 0; i < S; i++)
                {
                    GaussianVector[i] = simulator.Next();
                }
                ColumnVector Volterra_small = choleskyCorrel_Small * GaussianVector;
                //Adjusting the variance of Volterra Processus
                for (int i = 0; i < S; i++)
                {
                    Volterra_small[i] = Volterra_small[i] * Math.Sqrt((Math.Pow(grid.t(i), 2 * H) - Math.Pow(grid.t(i) - grid.t(0), 2 * H)) / (2 * H));
                }

                // Simulating VOlterra on t_8 ... t_N with the truncated Formula
                double[] Volterra = new double[N + 1];
                for (int i = 0; i <= N; i++)
                {
                    if (i < S)
                    {
                        Volterra[i] = Volterra_small[i];
                    }
                    //Tranceted Formula
                    else
                    {
                        Volterra[i] = Math.Sqrt(covM[i, i]) * (Correl[i, i - 1] * Volterra[i - 1] / Math.Sqrt(covM[i - 1, i - 1]) + Math.Sqrt(1 - Math.Pow(Correl[i, i - 1], 2)) * simulator.Next());
                    }
                }

                double VIX_ = VIX_Calculate(epsilon, grid, Volterra);
                VIX += VIX_;
            }
            //sw.Close();
            VIX /= MC;
            TimeSpan dur = DateTime.Now - start;
            return(VIX);
        }