function APut=AP(S,S0,N,M,sigma,u,K,r)
dt=1/N;

for j=2:N-1
    P(j,:)=ploy(S,S0,N,M,sigma,u,K,r,j);
end

for i=1:M
    for j=2:N
        if j==N
            AP(i)=max(K-S(i,j))*exp(-u*j*dt);
        else
            CV=P(j,1)*S(i,j)^2+P(j,2)*S(i,j)+P(j,1);
            EV=K-S(i,j);
            if EV>=CV
                AP(i)=EV*exp(-u*j*dt);
                break
            end
        end
    end
end

APut=sum(AP)/M;