public double MSPriceBS(double S, double K, double T, double sigma, double r, double q, int MaxIter, double Tol, double b, double dt)
{
MSsetBS mssettings = new MSsetBS();
mssettings.theta = Math.Log(K / S) / sigma / Math.Sqrt(T);
mssettings.K = K;
mssettings.sigma = sigma;
mssettings.r = r;
mssettings.q = q;
mssettings.T = T;
Tol = 1e-5;
MaxIter = 50;
double a = Math.Max(1.25, 0.95 * mssettings.theta);
b = 3.0;
// Golden section search method to find y
GoldenSearch GS = new GoldenSearch();
double y = GS.GoldenSearchBS(a, b, Tol, MaxIter, mssettings);
// Bisection algorithm to find y
//double y = BisectionBS(mssettings,a,b,Tol,MaxIter,dt);
if (y < mssettings.theta)
{
y = mssettings.theta;
}
MSExpansionBS MS = new MSExpansionBS();
return(MS.MSPutBS(y, mssettings));
}
public double[] MSPriceHeston(HParam param, OpSet opset, MSSet msset)
{
// param = Heston parameters
// opset = option settings
// msset = Medvedev-Scaillet expansion settings
// Extract quantities from the option settings
double K = opset.K;
double S = opset.S;
double v0 = param.v0;
double T = opset.T;
double r = opset.r;
double q = opset.q;
// Extract quantities from the MS structure
int N = msset.N;
double a = msset.a;
double b = msset.b;
double A = msset.A;
double B = msset.B;
double dt = msset.dt;
double tol = msset.tol;
int MaxIter = msset.MaxIter;
int NumTerms = msset.NumTerms;
double yinf = msset.yinf;
int method = msset.method;
// Closed-form European put
NewtonCotes NC = new NewtonCotes();
double EuroPutClosed = NC.HestonPriceNewtonCotes(param, opset, method, A, B, N);
// Moneyness
double theta = Math.Log(K / S) / Math.Sqrt(v0) / Math.Sqrt(T);
// Find the barrier level
// Bisection method to find y
// a = Math.Max(1.25,0.95*theta);
// b = 3.0;
// double y = BisectionMS(a,b,theta,K,param,r,q,T,NumTerms,tol,MaxIter,dt);
// Golden section search method to find y
GoldenSearch GS = new GoldenSearch();
a = 1.5;
b = 2.5;
double y = GS.GoldenSearchMS(a, b, tol, MaxIter, K, param, theta, r, q, T, NumTerms);
if (y < theta)
{
y = theta;
}
// Find the early exercise premium
MSExpansionHeston MS = new MSExpansionHeston();
double AmerPutMS = MS.MSPutHeston(y, theta, K, param, r, q, T, NumTerms);
double EuroPutMS = MS.MSPutHeston(yinf, theta, K, param, r, q, T, NumTerms);
double EEP = AmerPutMS - EuroPutMS;
// Control variate American put
double AmerPut = EuroPutClosed + EEP;
// Output the results
double[] output = new double[6];
output[0] = EuroPutClosed;
output[1] = AmerPutMS;
output[2] = AmerPut; // Medvedev and Scaillet recommend this one.
output[3] = EEP;
output[4] = theta;
output[5] = y;
return(output);
}