Finite Difference method for American put option
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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);
1 个评论
Walter Roberson
2011-4-19
It would probably help to post a link that explains the difference between European and American put options.
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Greg
2011-4-27
0 个投票
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
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