clear
xvalue = zeros(1,10000); %initialize matrix for w values obtained for each iteration at t=.5
meanxmatrix = zeros(1,10000); %initialize matrix for mean
difference = zeros(1,10000);  %initialize matrix for difference
expectedcall = zeros(1,10000); %initialize matrix for expected value

for j = 1:10000 %iterate through at least 10,000 repititions
    [t,w]=euler_maruyama([0,.5],12,100);
    xvalue(j) = w(101); %collect the w value at t=.5 for each iteration
    meanxmatrix(j) = 1;
    if xvalue(j)>15
        difference(j) = xvalue(j)-15;
    else
        difference(j) = 0;
    end
    j = j+1;
end

meanxvalue = mean(difference);  
expectedcallvalue = exp(-.05*.5)*meanxvalue  %compute the expected value of the call

meanxmatrix = meanxmatrix*meanxvalue;  %compute a matrix with the mean x value in every entry

figure() %plot difference along with mean
plot(difference)
hold on
plot(meanxmatrix,'ro')
title('Plot of Call Values vs. Iteration Number')
ylabel('max(X(t)-K,0) i.e. max(stock price - call price,0)')
xlabel('Iteration Number')
hold off