

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 
Salary Surveys 
Health Actuary Jobs 
Actuarial Recruitment 
Casualty Jobs 
Investment / Financial Markets Old Exam MFE Forum 

Thread Tools  Search this Thread  Display Modes 
#1




SOA sample question 75
You are using Monte Carlo simulation to estimate the price of an option X, for
which there is no pricing formula. To reduce the variance of the estimate, you use the control variate method with another option Y, which has a pricing formula. You are given: (i) The naive Monte Carlo estimate of the price of X has standard deviation 5. (ii) The same Monte Carlo trials are used to estimate the price of Y. (iii) The correlation coefficient between the estimated price of X and that of Y is 0.8. Calculate the minimum variance of the estimated price of X, with Y being the control variate. In the solution, they just use the formula Var(X*) = Var(Xbar)(1rho^2), but why do they not use the formula Var(X*) = Var(Xbar) + beta^2(Var(Ybar))  2betaCov(Xbar,Ybar)? Is it because Var(Ybar) is not given which makes calculating covariance impossible? Then again, the question didn't say that beta is set to minimize Var(x*), or does that not matter? 
#2




If you solve for the beta that minimizes the variance and plug in you should get the given formula after simplification.

Tags 
monte carlo 
Thread Tools  Search this Thread 
Display Modes  

