FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A analyst uses a control variate to price an Asian option. The simulated Asian option payoff X has variance 36 and the control variate Y (a European option with known analytic price) has variance 16. The correlation between X and Y is 0.80. Using the optimal coefficient, by what percentage is the variance of the controlled estimator reduced relative to the uncontrolled estimator?
The variance falls by 64%. With the optimal control variate coefficient, the remaining variance equals the original variance times one minus the squared correlation, so a correlation of 0.80 removes 0.64 of the variance, regardless of the individual variances.
- A80%
- B36%
- C64%Correct
- D20%
Explanation
With the optimal coefficient, the variance becomes Var(X)(1 - rho^2) = 36 x (1 - 0.64) = 12.96. The reduction is rho^2 = 64%. Using 80% mistakes rho for rho^2.
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