%rouwenhorst.m
%
%[zgrid, P] = rouwenhorst(rho, sigma_eps, n)
%
% rho is the 1st order autocorrelation
% sigma_eps is the standard deviation of the error term
% n is the number of points in the discrete approximation
%
% http://www.karenkopecky.net/rouwenhorst.m

function [zgrid, P] = rouwenhorst(rho,sigma_eps,n)

mu_eps = 0;

q = (rho+1)/2;
nu = ((n-1)/(1-rho^2))^(1/2) * sigma_eps;

P = [q 1-q;1-q q];


for i=2:n-1
   P = q*[P zeros(i,1);zeros(1,i+1)] + (1-q)*[zeros(i,1) P;zeros(1,i+1)] + ...
       (1-q)*[zeros(1,i+1); P zeros(i,1)] + q*[zeros(1,i+1); zeros(i,1) P];
   P(2:i,:) = P(2:i,:)/2;
end

zgrid = linspace(mu_eps/(1-rho)-nu,mu_eps/(1-rho)+nu,n);