complete.m

有限差法计算期权价格

function value=complete(S0,K,T,r,delta,v)


q=2*r/(v^2); 
q2=2*(r-delta)/(v^2);



xmin=-5; 
xmax=5;
m=100;
vmax=m;
dx=(xmax-xmin)/m; 
dtau=(0.5*v^2*T)/vmax;
lambda=dtau/(dx^2); 
alpha=0.5*lambda;


for i=1:m
    w(i)=W((xmin+i*dx),q2);
    V(i)=w(i);
end

for j=1:m
    tau=dtau*j;
    
    b(1)=w(1)+0.5*lambda*(w(2)-2*w(1)+g((xmin+dx),(tau-dtau),q,q2))+0.5*lambda*g((xmin+dx),tau,q,q2);   
    for i=2:m-2
        
        b(i)=w(i)+0.5*lambda*(w(1+i)-2*w(i)+w(i-1));
    end
    b(m-1)=w(m-1)+0.5*lambda*(g(xmax,(tau-dtau),q,q2)-2*w(m-1)+w(m-2))+0.5*lambda*g((xmin+dx*m),tau,q,q2);
    
     
    
    
    Error=-10^(-5);
    sum=1;
    while sqrt(sum)>Error
       sum=0; 
       Error=10^(-5);
       Vnew(1)=0;
        for i=1:m-1           
            rho=(b(i)+alpha*(Vnew(i)+V(i+1)))/(1+2*alpha);
            Vnew(i+1)=max((V(i)+(rho-V(i))),g((xmin+dx*i),tau,q,q2));
            sum=sum+(Vnew(i+1)-V(i))^2;
        end
        for i=1:m-1
        V(i)=Vnew(i+1);
        end
    end
    for i=1:m-1
        
        w(i)=V(i);
    end
end
        



x0=log(S0/K);
j=fix((x0-xmin)/dx);
value = K*exp(-0.5*(q2-1)*x0)*exp(-(0.25*(q2-1)^2+q)*0.5*v^2*T)*w(j);

function [w2]=W(x,q2)

    w2=max((exp(0.5*x*(q2+1))-exp(0.5*x*(q2-1))),0);


function [g2]=g(x,tau,q,q2)

    g2=exp(0.25*tau*((q2-1)^2+4*q))*max((exp(0.5*x*(q2+1))-exp(0.5*x*(q2-1))),0);