Explanation

Let's analyze each option:

Option A: Incorrect

• The age-weighted historical simulation approach is a non-parametric method that does not incorporate GARCH model estimates. GARCH is a parametric approach for volatility modeling, while age-weighted historical simulation focuses on weighting historical observations differently based on their age.

Option B: Correct

• When the decay factor (λ) is close to 1, it means that older observations receive weights that are nearly as large as recent observations. This indicates persistence in the data set, as historical patterns continue to influence current risk estimates significantly.

Option C: Incorrect

• The correct weight formula for age-weighted historical simulation is: $\omega_{(i)} = \frac{\lambda^{i-1}(1 - \lambda)}{1 - \lambda^n}$ where n is the total number of observations, not i. The denominator should be 1 - λ^n, not 1 - λ^i.

Option D: Incorrect

• While having at least 250 observations is generally recommended for VaR calculations, this is not a specific requirement of the age-weighted historical simulation approach. The minimum number of observations depends on the desired confidence level and the specific application.

Therefore, option B is the most accurate statement about the age-weighted historical simulation approach.