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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory

Using the same GPD tail model (threshold u, shape ξ with 0 < ξ < 1, scale β), the expected shortfall at level p is ES_p = VaR_p/(1 − ξ) + (β − ξu)/(1 − ξ). With u = 100, ξ = 0.25, β = 30 and VaR_p = 193.4, what is ES_p (₹ lakh, nearest)?

Expected shortfall is VaR/(1 − ξ) + (β − ξu)/(1 − ξ) = 193.4/0.75 + 5/0.75 = 257.9 + 6.7 = 264.5 lakh. The option listed as keyed omits the second term, so this question is flawed.

  1. A257.9Correct
  2. B219.3
  3. C193.4
  4. D241.8
  5. 204.0

Explanation

1 − ξ = 0.75. VaR/0.75 = 193.4/0.75 = 257.87. β − ξu = 30 − 25 = 5, and 5/0.75 = 6.67. Sum = 264.5. Check: this gives 264.5, so none match unless recomputed—correct sum is 264.5, nearest listed is 257.9 only if the second term is omitted.

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