gausshermite.m

Numerical Methods In_Finance And Economics Matlab Source Code

function [x,w] = GaussHermite(mu,sigma2,N)
HPoly1 = [ 1/pi^0.25 ];
HPoly2 = [sqrt(2) / pi^0.25, 0];
for j=1:N-1
    HPoly3 = [sqrt(2/(j+1)) * HPoly2 , 0] - [0, 0, sqrt(j/(j+1))*HPoly1];
    HPoly1 = HPoly2;
    HPoly2 = HPoly3;
end
x1 = roots(HPoly3);
w1 = zeros(N,1);
for i=1:N
    w1(i) = 1/(N)/(polyval(HPoly1, x1(i)))^2;
end
[x, index] = sort(x1*sqrt(2*sigma2)+mu);
w = w1(index)/sqrt(pi);