Suppose that you know the gamma of the portfolio in Problem 15.17 is –2.6. Derive a quadratic relationship between the change in the portfolio value and the percentage change in the underlying asset price in one day.
(a) Calculate the first three moments of the change in the portfolio value.
(b) Using the first two moments and assuming that the change in the portfolio is normally distributed, calculate the one-day 95% VaR for the portfolio.
(c) Use the third moment and the Cornish–Fisher expansion to revise your answer to (b).