-19 Suppose that you know that the gamma of the portfolio in Problem 14.18 (again measured with respect to actual changes) is 2.6. What is the gamma with respect to proportional changes? Derive a quadratic relationship between the change in the portfolio value and the percentage change in the underlying asset price in one day. (a) Use Isserlis' theorem to 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) hree-year bond as well 14.18 Consider a portfolio of options on a single asset. Suppose that the delta of the portfolio (calculated with respect to actual changes) is 12, the value of the asset is $10, and the daily volatility of the asset is 2%. What is the delta with respect to proportional changes? Estimate the one-day 95% VaR for the portfolio from the delta -19 Suppose that you know that the gamma of the portfolio in Problem 14.18 (again measured with respect to actual changes) is 2.6. What is the gamma with respect to proportional changes? Derive a quadratic relationship between the change in the portfolio value and the percentage change in the underlying asset price in one day. (a) Use Isserlis' theorem to 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) hree-year bond as well 14.18 Consider a portfolio of options on a single asset. Suppose that the delta of the portfolio (calculated with respect to actual changes) is 12, the value of the asset is $10, and the daily volatility of the asset is 2%. What is the delta with respect to proportional changes? Estimate the one-day 95% VaR for the portfolio from the delta