r=0.02;
sigma=0.3;
T=1;
x=100;
K=200;

function [res]=f(g)
   d=prod(size(g));
   S_T=zeros(1,d);
   S_T=x .* exp((r - sigma*sigma/2)*T*ones(1,d)+sigma*sqrt(T)*g);
   res=exp(-r*T)*max(S_T-K,0);
endfunction

function res=approx_variance(lambda)
   Y=f(G).^2 .* exp(-lambda*G+lambda^2/2);
   res=mean(Y)-mean(f(G))^2;
endfunction

K=100;
lambda=[0.0:0.05:3.0];
z=0;
G=grand(1,n,"nor",0,1);
for i=[1:prod(size(lambda))] do
	z(i)=approx_variance(lambda(i));
end;
plot2d(lambda,z);

K=200;
z=0;
lambda=[0:0.05:6];
G=grand(1,n,"nor",0,1);
for i=[1:prod(size(lambda))] do
	z(i)=approx_variance(lambda(i));
end;
plot2d(lambda,z);