Question 5

A bank has written a European call option on one stock and a European put on another stock. For the first option, the stock price is 98, the strike price is 85, the volatility is 45% per annum, and the time to maturity is ten months. For the second option, the stock price is 28, the strike price is 18, the volatility is 36% per annum, and the time to maturity is 1 year. Neither stock pays a dividend, the risk-free rate is 6% per annum, and the correlation between stock returns is 0.6.

a. What are the deltas for the European call and put options, respectively?

b. What is the approximately linear relationship between the change in the portfolio value P and the stock returns, x₁ and x₂?

c. Calculate a 10-day 99% VaR and ES using only deltas.