%
% Vectorized version, uses shifts via colon notation.
%%%%%%%%%% Problem and method parameters %%%%%%%%%%%%%
S = 5;E = 10;T = 1;r = 0.06;sigma = 0.3;M = 256;
dt = T/M;A = 0.5*(exp(-r*dt)+exp((r+sigma^2)*dt));
u=A+ sqrt(A^2-1);d = 1/u;p = (exp(r*dt)-d)/(u-d);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Option values at time T
W = max(E-S*d.^([M:-1:0]').*u.^([0:M]'),0);
histogram(W,50);
title('Underlying Price at Maturity')

% Re-trace to get option value at time zero
q = 1-p;
for i = M:-1:1
W = p*W(2:i+1) + q*W(1:i);
end
W = exp(-r*T)*W;