Explanation:
Expected Shortfall (ES) at a given confidence level is the expected loss given that the loss exceeds the VaR at that confidence level. It can be estimated discretely as the simple average of the VaR estimates for confidence levels in the tail region (from to $100\%$).
Using the 5 equal-probability slices in the $2.5\%(VaR_{97.5\%} + VaR_{98.0\%} + VaR_{98.5\%} + VaR_{99.0\%} + VaR_{99.5\%}) / 5$
ES =
ES = $1,988,880,000 / 5 = 397,776,000$
This is closest to JPY 398 million, which corresponds to Option A.
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| Confidence Level | VaR (JPY) |
|---|---|
| 95.0% | 332,760,000 |
| 95.5% | 336,292,500 |
| 96.0% | 340,095,000 |
| 96.5% | 350,332,500 |
| 97.0% | 359,107,500 |
| 97.5% | 367,882,500 |
| 98.0% | 378,412,500 |
| 98.5% | 392,452,500 |
| 99.0% | 410,880,000 |
| 99.5% | 439,252,500 |
What is the closest estimate of the daily ES at the 97.5% confidence level?
A
JPY 398 million
B
JPY 400 million
C
JPY 405 million
D
JPY 497 million
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