Hi all,i try to write a code about Monte Carlo simulation of Heston Model for european call price in Matlab, but there is some problem that i can not figure it out!can anyone help me?regards.function [European_call] = Monte_Carlo_HestonK = 100;T = 1;S = 100;sigma = 0.2;r = 0.06;div = 0.03;alpha = 5.0;Vbar = 0.20;Xi = 0.02;N = 52;M = 10000;dt = T/N;rho=-0.5;sdt = sqrt(dt);sum_CT = 0;sum_CT2 = 0;for j = 1:M St1 = S; St2 = S; Vt = sigma^2; eps1 = randn(N,1); eps2 = randn(N,1); eps3 = rho*eps1 + sqrt(1-rho^2)*eps2; for i = 1:N Vtn = Vt + alpha*(Vbar-Vt)*dt + Xi*sqrt(Vt)*sdt*eps3(i,1); Vt = Vtn; Vt = abs(Vt); %prevents negative volatilities Stn1 = St1 + (r-div)*St1*dt + sqrt(Vt)*St1*sdt*eps2(i,1); Stn2 = St2 + (r-div)*St2*dt + sqrt(Vt)*St2*sdt*-eps2(i,1); St1 = Stn1; St2 = Stn2; end CT = 0.5*(max(St1 - K , 0)+ max(St2 - K , 0)); sum_CT = sum_CT + CT; sum_CT2 = sum_CT2 + CT^2;endEuropean_call = sum_CT/M*exp(-r*T)SD = sqrt((sum_CT2 - (sum_CT^2)/M)*exp(-2*r*T)/(M-1));SE = SD/sqrt(M)

The code seems ok, except maybe that rho is not defined anywhere.What is the problem exatly ?

hi Antonio,i just forgot to write rho here. the problem is, this code can not give the right price. i used option city calculator to see the price of option.when alpha and Xi is zero, the code gives right price. but if i change those parameters, price goes wrong.

Stn1 and Stn2 should use eps1 not eps2

i can not understand what is the difference between eps1 and eps2 but now it works great!thanks for the tip Sonyah.

eps1 and eps2 are both random normals but its important to get them the right way round when using eps3, which should be the correlated random with eps1. Its probably a good idea for you to read a bit about multi-factor Monte Carlo and correlated random numbers - Hull has a good basic section about it.

thanks sonyah,i will read that part.