You are given a portfolio of options on a single underlying asset with a current value $100. The delta of this portfolio is 80, and daily asset returns have a mean of 0.5% and volatility of 2.0%.

a. Assuming that daily returns are normally distributed and uncorrelated, estimate the ten-day, 99% VaR for the portfolio. Note that z0.99 = 2.326. [Hint: What is the distribution of 10-day returns? Then, Var0.99 is the percentile L0.99 for losses, and L0.99=|G0.01| where G is from the gain distribution from returns]

b. Repeat Part a using a Cornish-Fisher expansion, assuming that the distribution of 10-day asset returns has an estimated skewness of = -0.6 and kurtosis = 3.5. [Hint: Since P is a constant times the 10-day return, the skewness and kurtosis of 10-day returns equal the skewness and kurtosis of P. Again work with G0.01]