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Answer: When simulating asset returns using Monte Carlo simulation, a sufficient number of trials must be used to ensure simulated returns are risk neutral.
## Explanation Statement B is invalid because: - **Risk neutrality** is not achieved by simply increasing the number of trials in Monte Carlo simulation. Risk neutrality is a concept related to derivative pricing where we adjust the probability measure to make the expected return equal to the risk-free rate. - The number of trials in Monte Carlo simulation affects the **precision and convergence** of the results, not the risk-neutral property. - To achieve risk neutrality in Monte Carlo simulation for derivative pricing, we typically use the **risk-neutral valuation framework** where we simulate asset prices under the risk-neutral probability measure, not by increasing the number of trials. **Analysis of other statements:** - **Statement A**: Correct - Historical simulation is indeed a nonparametric method that uses actual historical data without assuming a specific distribution. - **Statement C**: Correct - Bootstrapping preserves the correlation structure and distributional characteristics of the original data but typically assumes independence (no autocorrelation) between observations. - **Statement D**: Correct - Monte Carlo simulation is widely used for derivative pricing and scenario analysis in finance.
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Which of the following statements about simulation is invalid?
A
The historical simulation approach is a nonparametric method that makes no specific assumption about the distribution of asset returns.
B
When simulating asset returns using Monte Carlo simulation, a sufficient number of trials must be used to ensure simulated returns are risk neutral.
C
Bootstrapping is an effective simulation approach that naturally incorporates correlations between asset returns and non-normality of asset returns, but does not generally capture autocorrelation of asset returns.
D
Monte Carlo simulation can be a valuable method for pricing derivatives and examining asset return scenarios.