// Heston Price by Gauss-Legendre Integration
public OutputMD HestonPriceGaussLegendreMD(HParam param, OpSet settings, double[] xGLe, double[] wGLe, double[] A, double tol)
{
int nA = A.Length;
int nX = xGLe.Length;
double[,] int1 = new double[nA, nX];
double[,] int2 = new double[nA, nX];
double[] sum1 = new double[nA];
double[] sum2 = new double[nA];
// Numerical integration
HestonPrice HP = new HestonPrice();
int nj = 0;
for (int j = 1; j <= nA - 1; j++)
{
// Counter for the last point of A used
nj += 1;
sum1[j] = 0.0;
for (int k = 0; k <= nX - 1; k++)
{
// Lower and upper and limits of the subdomain
double a = A[j - 1];
double b = A[j];
double X = (a + b) / 2.0 + (b - a) / 2.0 * xGLe[k];
int1[j, k] = wGLe[k] * HP.HestonProb(X, param, settings, 1) * (b - a) / 2.0;
int2[j, k] = wGLe[k] * HP.HestonProb(X, param, settings, 2) * (b - a) / 2.0;
sum1[j] += int1[j, k];
sum2[j] += int2[j, k];
}
if (Math.Abs(sum1[j]) < tol && Math.Abs(sum2[j]) < tol)
{
break;
}
}
// Define P1 and P2
double pi = Math.PI;
double P1 = 0.5 + 1.0 / pi * sum1.Sum();
double P2 = 0.5 + 1.0 / pi * sum2.Sum();
// The call price
double S = settings.S;
double K = settings.K;
double T = settings.T;
double r = settings.r;
double q = settings.q;
string PutCall = settings.PutCall;
double HestonC = S * Math.Exp(-q * T) * P1 - K * Math.Exp(-r * T) * P2;
// The put price by put-call parity
double HestonP = HestonC - S * Math.Exp(-q * T) + K * Math.Exp(-r * T);
// The output structure
OutputMD output = new OutputMD();
// Output the option price
if (PutCall == "C")
{
output.Price = HestonC;
}
else
{
output.Price = HestonP;
}
// Output the integration domain;
output.lower = A[0];
output.upper = A[nj];
// Output the number of integration points
output.Npoints = (nj + 1) * nX;
return(output);
}
static void Main(string[] args)
{
// 32-point Gauss-Legendre Abscissas and weights
double[] xGLe = new Double[32];
double[] wGLe = new Double[32];
using (TextReader reader = File.OpenText("../../GaussLegendre32.txt"))
{
for (int k = 0; k <= 31; k++)
{
string text = reader.ReadLine();
string[] bits = text.Split(' ');
xGLe[k] = double.Parse(bits[0]);
wGLe[k] = double.Parse(bits[1]);
}
}
// Heston parameters
HParam param = new HParam();
param.kappa = 2.0;
param.theta = 0.05;
param.sigma = 0.3;
param.v0 = 0.05;
param.rho = 0.45;
param.lambda = 0.0;
// Option price settings
OpSet settings = new OpSet();
settings.S = 100.0;
settings.K = 100.0;
settings.r = 0.05;
settings.q = 0.01;
settings.trap = 1;
settings.PutCall = "C";
settings.T = 0.5;
// Price by Simpson's rule
NewtonCotesPrice NCP = new NewtonCotesPrice();
int method = 3;
double a = 1e-10;
double b = 150;
int NS = 10000;
double PriceSimpson = NCP.HestonPriceNewtonCotes(param, settings, method, a, b, NS);
// Potential integration domain
double lo = 1e-10;
double hi = 150;
int N = 1000;
double dA = (hi - lo) / Convert.ToDouble(N);
double[] A = new double[N];
for (int j = 0; j <= N - 1; j++)
{
A[j] = lo + j * dA;
}
// The modified domain Gauss-Legendre price
HestonPriceMD HPMD = new HestonPriceMD();
double tol = 1e-6;
OutputMD output = HPMD.HestonPriceGaussLegendreMD(param, settings, xGLe, wGLe, A, tol);
double PriceMD = output.Price;
double lower = output.lower;
double upper = output.upper;
int Npoints = output.Npoints;
double errorMD = PriceMD - PriceSimpson;
// The price using Newton Cotes
double PriceNC = NCP.HestonPriceNewtonCotes(param, settings, method, lower, upper, Npoints);
double errorNC = PriceNC - PriceSimpson;
// Write the results
Console.WriteLine("Zhu Multi-Domain Integration Algorithm");
Console.WriteLine("-------------------------------------------");
Console.WriteLine("Multi-Domain tolerance {0:E3}", tol);
Console.WriteLine("Lower integration limit {0:E3}", lower);
Console.WriteLine("Upper integration limit {0:F3}", upper);
Console.WriteLine("Number of integration pts {0:0}", Npoints);
Console.WriteLine("-------------------------------------------");
Console.WriteLine("Method Price Error ");
Console.WriteLine("-------------------------------------------");
Console.WriteLine("{0:0}-point Simpson {1,10:F4}", N, PriceSimpson);
Console.WriteLine("Multi-Domain {0,10:F4} {1,10:F4}", PriceMD, errorMD);
Console.WriteLine("Newton-Cotes {0,10:F4} {1,10:F4}", PriceNC, errorNC);
Console.WriteLine("-------------------------------------------");
}
