MATLAB二叉树美式期权定价编程

二叉树美式期权m.file

function [Price] = BinomialAmer(s0,k,T,n,r,sigma,z)

% T expiration date

% n total number of periods

% k exercise price

% risk free interest rate

% sigma volatility of

% s0 present price

% z devidend

deltat = T/n;

u=exp(sigma*sqrt(deltat));

d=exp(-sigma*sqrt(deltat));

p=(exp((r-z)*deltat)-d)/(u-d);

q=1-p;

for j=1:n

for i=1:j+1

s(j,i)=s0*u^(j+1-i)*d^(i-1);

y(j,i)=max(k-s(j,i),0);

end

end

f=zeros(n,n);

for w=1:n

f(n-1,w)=max(y(n-1,w),exp(-r*deltat)*(p*y(n,w)+q*y(n,w+1)));

end

for g=n-2:-1:1

for h=1:g+1

f(g,h)=max(y(g,h),exp(-r*deltat)*(p*f(g+1,h)+q*f(g+1,h+1)));

end

end

Price=max(exp(-r*deltat)*(p*f(1,1)+q*f(1,2)),0);