FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A risk analyst estimates the price of a European option by Monte Carlo simulation with 10,000 independent paths and obtains a standard error of 0.40. To cut the standard error to 0.10 using plain Monte Carlo with no variance reduction, approximately how many paths are needed?
About 160,000 paths are needed. Monte Carlo standard error declines in proportion to one over the square root of the number of paths, so cutting it fourfold requires sixteen times as many simulations, which is 10,000 multiplied by 16.
- A20,000
- B40,000
- C160,000Correct
- D100,000
Explanation
Standard error falls with the square root of N. Reducing it by a factor of 4 (0.40 to 0.10) requires 16 times as many paths: 10,000 x 16 = 160,000. Choosing 40,000 confuses the factor of 4 in standard error with the factor in N.
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