Q.3993 To retrieve the value at risk (VaR) for the U.S stock market under the generalized extreme-value (GEV) distribution, a risk analyst uses the following equation which characterizes a heavy-tailed Fréchet distribution.

$$\text{VaR}_\alpha = \mu_n - \frac{\sigma_n}{\xi_n}[1 - (-n\ln(\alpha))^{-\xi_n}]$$

The analyst uses the following somewhat "realistic" parameters:

• Location, $\mu = 3.0\%$
• Scale, $\sigma = 0.80\%$
• Tail index, $\xi = 0.20\%$

If the sample size, $n = 100$, then which is nearest to the implied 99.90% VaR?