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IAI Actuarial Core Principles · Economic Modelling · Valuing benefit guarantees using simulation

A simulation of a guarantee payoff Y gives a sample variance of 400 (Rs lakh squared) per path. A control variate X, whose expected value is known exactly, has variance 100 and covariance with Y of 80 per path. Using the optimal coefficient, what is the variance of the controlled estimator per path?

The controlled variance per path is 336. The optimal coefficient is 80/100 = 0.8, and the variance reduction equals covariance squared over the control's variance, 6400/100 = 64, so 400 minus 64 leaves 336.

  1. A336Correct
  2. B320
  3. C304
  4. D380
  5. 256

Explanation

Optimal b = Cov/Var(X) = 80/100 = 0.8. Controlled variance = Var(Y) - Cov^2/Var(X) = 400 - 6400/100 = 400 - 64 = 336. Equivalently correlation squared is 0.16, so variance is 400 x 0.84 = 336.

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