We have three stocks whose dynamics under the risk-neutral measure follow: Si(t)dSi(t)=rdt+idWi(t) for i=1,2,3 and 0tT=0.25. The log-return processes of the stocks are correlated with covariance matrix: 0.02670.01690.02100.01690.02160.01580.02100.01580.0307. Let (S1(0),S2(0),S3(0))=(42,40,35) be the initial stock prices and r=0.15. a. Consider a basket option of the three stocks with where X(T)=(1/3)i=13Si(T). Compute a Monte Carlo estimate for the price V(0) without using any variance reduction technique. Present the standard error and lower and upper 95% confidence bands of your simulation. Also report your simulation run length (number of replications). b. Repeat part (a), using antithetic variates