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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

A risk manager simulates the 99% tail loss of a portfolio and finds that very few plain Monte Carlo draws fall in the extreme loss region. Which technique is designed to address this by sampling more often from the tail and reweighting the results?

Importance sampling is the right technique. It draws more samples from the rare tail region using an alternative distribution and then reweights each outcome by the likelihood ratio, so the estimate stays unbiased while tail accuracy improves.

  1. AAntithetic variates
  2. BImportance samplingCorrect
  3. CBootstrapping with replacement
  4. DIncreasing the number of control variates

Explanation

Importance sampling draws from an alternative distribution that places more weight on the rare tail region and corrects with likelihood-ratio weights, keeping the estimator unbiased. Antithetic variates do not target rare events, and bootstrapping resamples observed data rather than altering the sampling distribution.

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