Finite Difference method for American put option

I have the code for finite difference method for European put option and I need to make adjustments to this code so that it calculates the price of an American option instead of a European one. I did finite difference method in Excel about a year ago but I'm new to Matlab and haven't got a clue. I would really appreciate it if someone could tell me where in the code I should make the adjustments and what these adjustments are.

Here's the code:

function price = EuPutExpl(S0,K,r,T,sigma,Smax,dS,dt)

M = round(Smax/dS);

dS = Smax/M;

N = round(T/dt);

dt = T/N;

matval = zeros(M+1,N+1);

vetS = linspace(0,Smax,M+1);

veti = 0:M;

vetj = 0:N;

matval(:,N+1) = max(K-vetS,0);

matval(1,:) = K*exp(-r*dt*(N-vetj));

matval(M+1,:) = 0;

a = 0.5*dt*(sigma^2*veti - r).*veti;

b = 1 - dt*(sigma^2*veti.^2 + r);

c = 0.5*dt*(sigma^2*veti + r).*veti;

for j=N:-1:1

for i=2:M

matval(i,j) = a(i)*matval(i-1,j+1) + b(i)*matval(i,j+1)+c(i)*matval(i+1,j+1);

end

end

price = interp1(vetS, matval(:,1),S0);

[Walter Roberson]

It would probably help to post a link that explains the difference between European and American put options.

Answer 1

[Greg]

For a beginner, this is quite impressive code!

I suppose for an American Put, you will just need to compute whether the put value that you compute in each loop (i.e. matval(i,j)) is the maximum value in it's row (i.e. for a given strike level). If so, set the current value equal to the maximum of that row. Otherwise, leave as is.

Good luck, and please correct me if I've made any schoolboy errors!

Greg

[Julia]

I was actually able to figure it out on my own. But thanks anyway.

By the way, I did not write the code above, I took it from the book.