public double CZEuroCall(double S0, double tau, HParam param, double K, double rf, double q, double[] Xs, double[] Ws)
{
Complex i = new Complex(0.0, 1.0);
double xi = 0;
Complex psi = 0;
int Nx = Xs.Length;
double[] Int1 = new double[Nx];
double[] Int2 = new double[Nx];
Complex I1, I2;
// Compute the integrands
CharFun CF = new CharFun();
for (int k = 0; k <= Nx - 1; k++)
{
Complex phi = Xs[k];
I1 = Complex.Exp(-i * phi * Math.Log(K)) * CF.CZCharFun(S0, tau, xi, param, K, rf, q, phi, psi, 1) / (i * phi);
Int1[k] = Ws[k] * I1.Real;
I2 = Complex.Exp(-i * phi * Math.Log(K)) * CF.CZCharFun(S0, tau, xi, param, K, rf, q, phi, psi, 2) / (i * phi);
Int2[k] = Ws[k] * I2.Real;
}
// Define the probabilities
double pi = Math.PI;
double P1 = 0.5 + (1.0 / pi) * Int1.Sum();
double P2 = 0.5 + (1.0 / pi) * Int2.Sum();
// Return the call price
return(S0 * Math.Exp(-q * tau) * P1 - K * Math.Exp(-rf * tau) * P2);
}
// Double integral using trapezoidal rule
public double DoubleTrapezoidal(HParam param, double S0, double K, double tau, double rf, double q,
double b0, double b1, double[] X, double[] T, int funNum)
{
Complex i = new Complex(0.0, 1.0);
double a, b, c, d, qr = 0.0;
Complex fun1, fun2, fun3, fun4;
double g1, g2, g3, g4, term1, term2, term3;
int Nt = T.Length;
int Nx = X.Length;
// Select rate or dividend
if (funNum == 1)
{
qr = q;
}
else if (funNum == 2)
{
qr = rf;
}
double[,] Int = new double[Nt, Nx];
double sumInt = 0.0;
// Double trapezoidal rule
CharFun CF = new CharFun();
for (int t = 1; t <= Nt - 1; t++)
{
a = T[t - 1];
b = T[t];
for (int x = 1; x <= Nx - 1; x++)
{
c = X[x - 1];
d = X[x];
fun1 = Complex.Exp(-b0 * i * c) * CF.CZCharFun(S0, tau, a, param, K, rf, q, c, -b1 * c, funNum) / (i * c);
fun2 = Complex.Exp(-b0 * i * d) * CF.CZCharFun(S0, tau, a, param, K, rf, q, d, -b1 * d, funNum) / (i * d);
fun3 = Complex.Exp(-b0 * i * c) * CF.CZCharFun(S0, tau, b, param, K, rf, q, c, -b1 * c, funNum) / (i * c);
fun4 = Complex.Exp(-b0 * i * d) * CF.CZCharFun(S0, tau, b, param, K, rf, q, d, -b1 * d, funNum) / (i * d);
g1 = Math.Exp(qr * a) * fun1.Real;
g2 = Math.Exp(qr * a) * fun2.Real;
g3 = Math.Exp(qr * b) * fun3.Real;
g4 = Math.Exp(qr * b) * fun4.Real;
term1 = g1 + g2 + g3 + g4;
fun1 = Complex.Exp(-b0 * i * c) * CF.CZCharFun(S0, tau, (a + b) / 2.0, param, K, rf, q, c, -b1 * c, funNum) / (i * c);
fun2 = Complex.Exp(-b0 * i * d) * CF.CZCharFun(S0, tau, (a + b) / 2.0, param, K, rf, q, d, -b1 * d, funNum) / (i * d);
fun3 = Complex.Exp(-b0 * i * (c + d) / 2.0) * CF.CZCharFun(S0, tau, a, param, K, rf, q, (c + d) / 2.0, -b1 * (c + d) / 2.0, funNum) / (i * (c + d) / 2.0);
fun4 = Complex.Exp(-b0 * i * (c + d) / 2.0) * CF.CZCharFun(S0, tau, b, param, K, rf, q, (c + d) / 2.0, -b1 * (c + d) / 2.0, funNum) / (i * (c + d) / 2.0);
g1 = Math.Exp(qr * (a + b) / 2.0) * fun1.Real;
g2 = Math.Exp(qr * (a + b) / 2.0) * fun2.Real;
g3 = Math.Exp(qr * a) * fun3.Real;
g4 = Math.Exp(qr * b) * fun4.Real;
term2 = g1 + g2 + g3 + g4;
fun1 = Complex.Exp(-b0 * i * (c + d) / 2.0) * CF.CZCharFun(S0, tau, (a + b) / 2.0, param, K, rf, q, (c + d) / 2.0, -b1 * (c + d) / 2.0, funNum) / (i * (c + d) / 2.0);
term3 = Math.Exp(qr * (a + b) / 2.0) * fun1.Real;
Int[t, x] = (b - a) * (d - c) / 16.0 * (term1 + 2 * term2 + 4 * term3);
sumInt += Int[t, x];
}
}
return(sumInt);
}
// Double integral using Gauss-Legendre
public double DoubleGaussLegendre(double S0, double tau, HParam param, double K, double rf, double q, double b0, double b1,
double[] xt, double[] wt, double[] xs, double[] ws, double a, double b, double c, double d, int funNum)
{
Complex i = new Complex(0.0, 1.0);
int Nt = xt.Length;
int Ns = xs.Length;
double h1 = (b - a) / 2.0;
double h2 = (b + a) / 2.0;
double k1 = (d - c) / 2.0;
double k2 = (d + c) / 2.0;
double time, phi, realfun, qr = 0.0;
Complex fun;
// Select rate or dividend
if (funNum == 1)
{
qr = q;
}
else if (funNum == 2)
{
qr = rf;
}
double Int = 0.0;
// Double integral
CharFun CF = new CharFun();
for (int t = 0; t <= Nt - 1; t++)
{
time = h1 * xt[t] + h2;
for (int x = 0; x <= Ns - 1; x++)
{
phi = k1 * xs[x] + k2;
fun = Complex.Exp(-b0 * i * phi) * CF.CZCharFun(S0, tau, time, param, K, rf, q, phi, -b1 * phi, funNum) / (i * phi);
realfun = Math.Exp(qr * time) * fun.Real;
Int += h1 * k1 * wt[t] * ws[x] * realfun;
}
}
return(Int);
}