Financial Risk Manager Part 1

The 'Black Swan' problem is indeed the most significant limitation of bootstrapping. The term 'Black Swan' is used in the context of events that are beyond the realm of normal expectations and have potentially severe consequences. These events are characterized by their extreme rarity, severe impact, and the widespread insistence they were obvious in hindsight. In the context of bootstrapping, the 'Black Swan' problem refers to the inability of the bootstrap method to generate data that has not occurred in the sample. This is because bootstrapping is a resampling method that generates new samples by drawing observations from the original data. Therefore, it cannot create or predict 'Black Swan' events that are not represented in the original data. This limitation can lead to underestimation of risk or uncertainty in various applications, including financial risk management and predictive modeling.

Choice B is incorrect. Bootstrapping does not inherently construct samples that are significantly larger than historically observed datasets. The size of the bootstrapped samples is determined by the analyst and can be set to match the size of the original dataset. Therefore, this statement does not represent a limitation of bootstrapping.

Choice C is incorrect. While it's true that bootstrapping can be applied to data with time dependence features, it's not always suitable or accurate in these cases due to its assumption of independence between observations. However, this doesn't represent a significant limitation as there are variations of bootstrap methods designed specifically for time series data.

Choice D is incorrect. The use of antithetic variables isn't a requirement for bootstrapping; rather, it's an optional technique used in Monte Carlo simulations to reduce variance and improve efficiency. This choice seems to confuse two different statistical techniques and thus doesn't accurately reflect a limitation of bootstrapping.