有限差分方法对美式看涨期权定价
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2015-05-21
01:33:06
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function
[a,b,c,M,N,f,p,u]=finitedifferencemethod2(q,T,S0,K,L,r,sigma,dS,d
t)
K=100;
r=0.02;
q=0;
sigma=0.2;
dS=4;
S0=100;
T=1;
dt=1/200;
M=50;%M=L/dS,L=200(nearly double of S0=100);
N=200;%N=T/dt,T=1;
f=zeros(M+1,N+1);
for m=0:M
f(m+1,N+1)=max(m*dS-K,0);
end
for m=0:M
f(m+1,1)=S0;
end
for n=0:N
f(M+1,n+1)=(M*dS)*exp(-q*(T-n*dt))-K*exp(-r*(T-n*dt));
end
for n=0:N
f(1,n+1)=0;
end
a=zeros(M-1,1);
b=a;
c=a;
for m=1:M-1
a(m)=1/2*dt*(sigma^2*m^2-(r-q)*m);
b(m)=1-dt*(sigma^2*m^2+r);
c(m)=1/2*dt*(sigma^2*m^2+(r-q)*m);
end
for n=N:-1:1
for m=1:M-1
p(m+1,n)=max(0,m*dS-K);
u(m+1,n)=a(m)*f(m,n+1)+b(m)*f(m+1,n+1)+c(m)*f(m+2,n+1);
f(m+1,n)=max(p(m+1,n),u(m+1,n));
end
end
f(26,1)
plot(0:dS:M*dS,f(:,1))
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