// Accuracy of price on number of steps
public static Vector <double> Prices(TwoFactorBinomialParameters optionData, Vector <int> meshSizes, double S1, double S2)
{
// Caculates the price for a number of step sizes (usually increasing)
var result = new Vector <double>(meshSizes.Size);
for (var j = result.MinIndex; j <= result.MaxIndex; j++)
{
var local = new TwoFactorBinomial(optionData, meshSizes[j], S1, S2);
result[j] = local.Price();
}
return(result);
}
public TwoFactorBinomial(TwoFactorBinomialParameters optionData, int NSteps, double S1, double S2)
{
// The most important constuctor
par = optionData;
N = NSteps;
// Mesh sizes, Clewlow (2.43)-(2.44)
delta_T = par.T / N; // DeltaT
h1 = par.sigma1 * Math.Sqrt(delta_T); // DeltaX1
h2 = par.sigma2 * Math.Sqrt(delta_T); // DeltaX2
//cout << "deltas t, S... " << k << ", " << h1 << ", " << h2 << endl;
// Parameters (prob)
double nu1 = par.r - par.div1 - (0.5 * par.sigma1 * par.sigma1);
double nu2 = par.r - par.div2 - (0.5 * par.sigma2 * par.sigma2);
//cout << "nu1... " << nu1 << ", " << nu2 << endl;
double a = h1 * h2; double b = h2 * nu1 * delta_T; double c = h1 * nu2 * delta_T;
double d = par.rho * par.sigma1 * par.sigma2 * delta_T;
//cout << "a ..." << a << ", " << b << ", " << c << ", " << d << endl;
double disc = Math.Exp(-(par.r) * delta_T);
puu = disc * 0.25 * (a + b + c + d) / a; // eq. (2.45)
pud = disc * 0.25 * (a + b - c - d) / a;
pdu = disc * 0.25 * (a - b + c - d) / a;
pdd = disc * 0.25 * (a - b - c + d) / a;
//cout << "puu ..." << puu << ", " << pud << ", " << pdu << ", " << pdd << endl;
// Asset arrays
// Initialise asset prices at *maturity*. Norice that the start index is a negative number
asset1 = new Vector <double>(2 * N + 1, -N);
asset2 = new Vector <double>(2 * N + 1, -N);
asset1[-N] = S1 * Math.Exp(-N * h1);
asset2[-N] = S2 * Math.Exp(-N * h2);
double edx1 = Math.Exp(h1);
double edx2 = Math.Exp(h2);
//cout << "edx1... disc " << edx1 << ", " << edx2 << ", " << disc << endl;
for (int n = -N + 1; n <= N; n++)
{
asset1[n] = asset1[n - 1] * edx1;
asset2[n] = asset2[n - 1] * edx2;
}
//print(asset1);
//print(asset2);
option = new NumericMatrix <double>(2 * N + 1, 2 * N + 1, -N, -N);
// Calculate option price at the expiry date
for (int j = option.MinRowIndex; j <= option.MaxRowIndex; j += 2)
{
//cout << j << ", ";
for (int k = option.MinColumnIndex; k <= option.MaxColumnIndex; k += 2)
{
option[j, k] = Payoff(asset1[j], asset2[k]);
}
}
}
