// Medvedev-Scaillet price using expansion
public double[] MSPrice(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();
BisectionAlgo BA = new BisectionAlgo();
MSPut MS = new MSPut();
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
double y = BA.Bisection(a, b, theta, K, param, r, q, T, NumTerms, tol, MaxIter, dt);
if (y < theta)
{
y = theta;
}
// Find the early exercise premium
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;
output[3] = EEP;
output[4] = theta;
output[5] = y;
return(output);
}
// Derivative of the MS approximation
public double MSPutDiff(double y, double theta, double Strike, HParam param, double r, double q, double T, int NumTerms, double dy)
{
MSPut MS = new MSPut();
return((MS.MSPutHeston(y + dy, theta, Strike, param, r, q, T, NumTerms) - MS.MSPutHeston(y - dy, theta, Strike, param, r, q, T, NumTerms)) / 2.0 / dy);
}