
Explanation:
According to the Extreme Value Theory, the formula to calculate Value at Risk (VaR) utilizing the Generalized Extreme Value (GEV) distribution is:
For the 95% VaR (where ):
For the 99.5% VaR (where ):
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Q.52 Suppose that we are informed that in a U.S. stock market, denominated in % terms, the location parameter of the limiting distribution, , is 2%, the scale parameter, , is 0.6, and the tail index, , is 0.4. Apply these parameters in the Fréchet VaR formula to calculate the estimated 95% VaR and 99.5% VaR, respectively. Assume .
A
95% VaR: 1.340; 99.5% VaR: 1.657
B
95% VaR: 1.657; 99.5% VaR: 1.119
C
95% VaR: 1.28; 99.5% VaR: 2.477
D
95% VaR: 1.657; 99.5% VaR: 1.876
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