FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A risk team estimates the price of an option by Monte Carlo simulation with N independent draws, obtaining a sample standard deviation of discounted payoffs of USD 12. They want the half-width of a 95% confidence interval (using 1.96) for the price to be no more than USD 0.12. Approximately what minimum N is required?
About 38,416 draws are needed. The half-width of the 95% interval is 1.96 times 12 divided by the square root of N. Setting this at 0.12 gives a square root of N of 196, so N equals 196 squared, which is 38,416.
- A38,416Correct
- B384,160
- C3,842
- D196,000
Explanation
Half-width = 1.96 x 12 / sqrt(N) <= 0.12. So sqrt(N) >= 1.96 x 12 / 0.12 = 196, hence N >= 196^2 = 38,416. Using 196,000 treats sqrt(N) as N/1000 incorrectly, and 3,842 drops a factor of ten.
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