CoachThe delta–gamma approximation replaces full revaluation by the second-order expansion , with the first and second derivatives of the portfolio in the risk factors.
Exemples
Example 21.9 (One book, several numbers)
Over the last 500 days, historical simulation gives a one-day 99% VaR of USD 2.10 million; the EWMA delta-normal VaR is 1.58 million, the equal-weighted one 1.60 million, Monte Carlo with full revaluation on the EWMA covariance 1.66 million, and filtered historical simulation 2.09 million (Figure 21.1). Historical simulation with delta–gamma revaluation gives 2.10 million, delta alone 1.91: the short straddle’s gamma adds losses in both tails. The normal methods are lower because the historical moves have fatter tails than the normal.