FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
A Monte Carlo study of option prices uses 10,000 independent draws. The sample standard deviation of the discounted payoffs is 15 and the sample mean is 6.40. Using a 95% confidence level (critical value 1.96), what is the confidence interval for the true price?
The interval is 6.40 plus or minus 0.294. The standard error is 15 divided by 100, or 0.15, and multiplying by the 95% critical value of 1.96 gives a half-width of 0.294. Using only the standard error would understate the interval.
- A6.40 ± 0.294Correct
- B6.40 ± 29.4
- C6.40 ± 0.15
- D6.40 ± 2.94
Explanation
Standard error = 15 / sqrt(10,000) = 15/100 = 0.15. The interval half-width = 1.96 x 0.15 = 0.294. Option 6.40 ± 0.15 omits the critical value, while the others misplace the decimal by using wrong scaling of the standard error.
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