// Golden Section Search method for Black Scholes
public double GoldenSearchBS(double a, double b, double tol, int MaxIter, MSsetBS mssettings)
{
MSExpansionBS MS = new MSExpansionBS();
double x1, x2, x3, x4, f1, f2, f3, f4;
double GR = (Math.Sqrt(5.0) - 1.0) / 2.0;
int k = 0;
while (Math.Abs(b - a) > tol)
{
k = k + 1;
x1 = a;
x2 = a + (1.0 - GR) * (b - a);
x3 = a + GR * (b - a);
x4 = b;
f1 = -MS.MSPutBS(x1, mssettings);
f2 = -MS.MSPutBS(x2, mssettings);
f3 = -MS.MSPutBS(x3, mssettings);
f4 = -MS.MSPutBS(x4, mssettings);
if ((f1 > f2) & (f2 < f3))
{
b = x3;
}
else if ((f2 > f3) & (f3 < f4))
{
a = x2;
}
if (k > MaxIter)
{
break;
}
}
return((a + b) / 2.0);
}
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));
}
// Derivative of the MS approximation
public double MSPutBSdiff(double y, MSsetBS mssettings, double dy)
{
MSExpansionBS MS = new MSExpansionBS();
return((MS.MSPutBS(y + dy, mssettings) - MS.MSPutBS(y - dy, mssettings)) / 2.0 / dy);
}
