
Answer-first summary for fast verification
Answer: The bootstrapping methods, either naïve or sophisticated, rely upon the underlying assumption that the data are iid.
## Explanation Let's analyze each statement: **Statement A**: Correct. In option pricing using Monte Carlo simulation, we typically work in a risk-neutral world where the stock price follows a risk-neutral process (e.g., geometric Brownian motion with risk-free rate as the drift). **Statement B**: Correct. Bootstrapping indeed generates observation indices by randomly sampling with replacement from the original dataset. **Statement C**: **Incorrect**. While basic bootstrapping methods assume iid (independent and identically distributed) data, sophisticated bootstrapping methods like block bootstrap, moving block bootstrap, or stationary bootstrap are specifically designed to handle dependent data (time series data). These methods relax the iid assumption. **Statement D**: Correct. Monte Carlo simulation relies on the specified data generating process (DGP). If the DGP doesn't adequately capture the characteristics of the observed data (e.g., fat tails, volatility clustering, etc.), the simulation results may be unreliable. Therefore, statement C is incorrect because sophisticated bootstrapping methods do NOT rely on the iid assumption - they are specifically designed for dependent data.
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Which of the following statement is incorrect regarding the Monte Carlo simulation and bootstrapping?
A
In pricing the option, the Monte Carlo simulation assumes a risk-neutral stock price process to simulate the paths.
B
The bootstrap generates observation indices by randomly sampling with replacement.
C
The bootstrapping methods, either naïve or sophisticated, rely upon the underlying assumption that the data are iid.
D
If the specified data generating process does not adequately describe the observed data, then the Monte Carlo simulation may be unreliable.