FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
An analyst estimates the price of a European call option by running Monte Carlo simulation with 10,000 independent paths and obtains a standard error of 0.40. Holding everything else constant, approximately how many paths are needed to reduce the standard error to 0.10?
About 160,000 paths are needed. Monte Carlo standard error falls with the square root of the number of paths, so reducing it by a factor of four requires sixteen times as many simulations, which is 16 times 10,000, or 160,000.
- A20,000
- B40,000
- C160,000Correct
- D100,000
Explanation
Standard error scales with 1/sqrt(N). Cutting 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 paths. Choosing 40,000 wrongly scales N linearly with the error reduction factor.
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