FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A risk analyst estimates the price of a derivative by running 10,000 independent Monte Carlo trials and obtains a standard error of 0.40. She wants the standard error to fall to 0.10, and all other settings are unchanged. Approximately how many trials are needed?
About 160,000 trials are needed. Monte Carlo standard error falls with the square root of the number of trials, so cutting the error to one quarter requires 16 times as many simulations. Multiplying 10,000 by 16 gives 160,000 trials.
- A40,000
- B100,000
- C160,000Correct
- D20,000
Explanation
Standard error scales with 1/sqrt(N). Reducing it from 0.40 to 0.10 is a factor of 4, so N must rise by 4^2 = 16, giving 10,000 x 16 = 160,000. Quadrupling the trials to 40,000 only halves the error to 0.20.
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