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Finding variance with a control variable
A monte carlo valuation is run using the control variate method. The estimated variance of the variable being estimated is 8. The estimate of the variance of the control variable is 12. The estimated covariance is 9.
Determine the difference in the number of simulations required so that the estimated mean is within .05 of the true mean 90% of the time between the valuation of with the naive monte carlo methods and valuation using the control variate method. So let X but the variable were estimating and Y the control. Im guessing that Var(X) = 8, Var(Y) = 12 and Cov(X,Y)=9. my work: https://imgur.com/a/a6Gan answer: https://imgur.com/a/1BhaO Why are they saying the control variance is 2 and not 2/n which is what the formula in the manual says it should be? Thanks in advance! 
#2




By definition:
y* = control variate ybar= Monte Carlo estimate for option y xbar= Monte Carlo estimate for option x x = true price of option x "The estimated variance of the variable being estimated is 8. The estimate of the variance of the control variable is 12. The estimated covariance is 9." Means: Var[xbar] = 8 Var[ybar] = 12 Cov[xbar,ybar] = 9 Not: Var(X) = 8, Var(Y) = 12 and Cov(X,Y)=9 Thus you don't divide by n. 
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