FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A Monte Carlo simulation estimates an option price with a standard error of 0.40 using 2,500 independent trials. The analyst wants the standard error reduced to 0.10 with no variance reduction technique. Approximately how many trials are needed?
About 40,000 trials are needed. Monte Carlo standard error falls with the square root of the number of trials, so cutting it from 0.40 to 0.10, a factor of four, requires sixteen times as many trials: 2,500 times 16 equals 40,000.
- A10,000
- B40,000Correct
- C20,000
- D5,000
Explanation
Standard error scales with 1/sqrt(N). Reducing it by a factor of 4 (0.40/0.10) requires N to increase by 4^2 = 16. So 2,500 x 16 = 40,000. The 10,000 option wrongly multiplies by 4.
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