static void Main(string[] args)
{
//Ploting results Graph
//Application.EnableVisualStyles();
//Application.SetCompatibleTextRenderingDefault(false);
//Application.Run(new Graph());
rBergomiVIXfuture model = new rBergomiVIXfuture();
Func <double, double> epsilon_0 = t => Math.Pow(0.235, 2);// *Math.Sqrt(1 + t);
double T = 2.0;
//// the Gri t_0 ..... t_{100} = T
int n = 500;
Grid grid = new Grid(0, T, (int)Math.Abs(T * n));
//lognormal
double vixfuture_LogNormal = model.VIXfuture_LogNormal(grid.t(35), epsilon_0);
// //Mc with hybrid Scheme
ColumnVector vixfuture_Hybrid = model.VIXfuture_HybridMethod(T, epsilon_0);
ColumnVector newvixfutures = new ColumnVector(vixfuture_Hybrid.Count());
ColumnVector newvixlognorm = new ColumnVector(vixfuture_Hybrid.Count());
ColumnVector newvixtruncated = new ColumnVector(vixfuture_Hybrid.Count());
ColumnVector ti = new ColumnVector(vixfuture_Hybrid.Count());
int perdiod = 100;
for (int i = 0; i < vixfuture_Hybrid.Count(); i++)
{
int N_i = (i + 1) * perdiod;
ti[i] = grid.t((N_i));
newvixfutures[i] = vixfuture_Hybrid[i];
newvixtruncated[i] = model.VIXfuture_TruncatedChlsky(ti[i], epsilon_0);
newvixlognorm[i] = model.VIXfuture_LogNormal(ti[i], epsilon_0);
}
Application.Run(new Plot(ti, newvixlognorm, newvixfutures, newvixtruncated));
//Application.Run(new Plot(ti, newvixfutures,newvixlognorm, "Volterra Simulation in hybrid Method", "T + Delta ", "V", "volterra process"));
//Application.Run(new Plot(ti, newvixlognorm, "Volterra Simulation in hybrid Method", "T + Delta ", "V", "volterra process"));
// //Mc with trancated Cholesky
double TrancatedMethode_MCstdDeviation;
double vixfuture_trancated = model.VIXfuture_TruncatedChlsky(T, epsilon_0, out TrancatedMethode_MCstdDeviation);
//S&P Option Pricing
VIXOption option = new VIXOption(VIXOption.OptionType.Call, 1.0, 100);
double optionPrice = model.PriceVIXOption(option, epsilon_0, 100);
} //Main
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);
}