Financial Risk Manager Part 1

The Black Swan problem is the most significant limitation of bootstrapping because the bootstrap method cannot generate data that has not occurred in the original sample. This means it cannot account for extreme events or outliers that haven't been observed historically.

Detailed Explanation:

1. Option A (Correct): The "Black Swan" problem refers to the bootstrap's inability to generate data points outside the range of the original sample. Since bootstrapping resamples from existing data, it cannot create new extreme values that haven't been observed before, making it vulnerable to rare, high-impact events.

2. Option B (Incorrect): This describes a limitation of simulation methods, not specifically bootstrapping. Bootstrapping creates samples of the same size as the original dataset by resampling with replacement.

3. Option C (Incorrect): This is actually an advantage of specialized bootstrapping methods like Circular Block Bootstrap (CBB) for time-dependent data, not a limitation.

4. Option D (Incorrect): Antithetic variables are a variance reduction technique used in Monte Carlo simulations, not in bootstrapping methods.

Key Takeaway: Bootstrapping's reliance on historical data means it cannot extrapolate beyond observed ranges, making it unsuitable for estimating probabilities of truly novel or extreme events.