A bank has written a call option on one stock and a put option on another stock. For the first option the stock price is 50, the strike price is 51, the volatility is 28% per annum, and the time to maturity is nine months. For the second option the stock price is 20, the strike price is 19, the volatility is 25% per annum, and the time to maturity is one year. Neither stock pays a dividend, the risk-free rate is 6% per annum, and the correlation between stock price returns is 0.4.

Calculate a 10-day 99% VaR:

a. Using only delta

b. Using delta, gamma, and the first two moments of the change in the portfolio value

c. Using delta, gamma, and the first three moments of the change in the portfolio value

d. Using the partial simulation approach

e. Using the full simulation approach