function [price, lattice] = LatticeAmPut(S0,X,r,T,sigma,N)
deltaT = T/N;
u=exp(sigma * sqrt(deltaT));
d=1/u;
p=(exp(r*deltaT) - d)/(u-d);
lattice = zeros(N+1,N+1);
for j=0:N
   lattice(N+1,j+1)=max(0 , X-S0*(u^j)*(d^(N-j)));
end
for i=N-1:-1:0
   for j=0:i
      lattice(i+1,j+1) = max( X-S0*u^j*d^(i-j) , ...
         exp(-r*deltaT) *(p * lattice(i+2,j+2) + (1-p) * lattice(i+2,j+1)));
   end
end
price = lattice(1,1);