Question 3 (6 marks) 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 35, the strike price is 35, the volatility is 20% per annum, and the time to maturity is nine months. For the second option the stock price is 45, the strike price is 40, the volatility is 25% per annum, and the time to maturity is one year. Neither stock pays a dividend, the risk-free rate is 3% per annum, and the correlation between stock price returns is 0.5. Calculate a 10-day 99% VAR for the portfolio of the options. (a) Using the partial simulation approach with 100 random samples (b) Using the full simulation approach with 100 random samples Requirements: You can use either Excel, VBA or MATLAB for this question. Ensure to clearly comment on each step and clearly indicate the final answer. Hint for Question 3: You need to simulate 2 sets of random daily returns for the two stocks with correlation of 0.3. To simulate correlated normal random variables, first simulate 2 sets of independent standard normal variables (with mean of zero and standard deviation of 1), 21 and 22. The daily return for the first stock will be x = mean(x) + stdev(x) + 2 . The daily return for the second stock will be y = mean(y) + stdev(y) * [218+22/(1 - p2)]. As per normal practice, use zero for the mean daily returns. Question 3 (6 marks) 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 35, the strike price is 35, the volatility is 20% per annum, and the time to maturity is nine months. For the second option the stock price is 45, the strike price is 40, the volatility is 25% per annum, and the time to maturity is one year. Neither stock pays a dividend, the risk-free rate is 3% per annum, and the correlation between stock price returns is 0.5. Calculate a 10-day 99% VAR for the portfolio of the options. (a) Using the partial simulation approach with 100 random samples (b) Using the full simulation approach with 100 random samples Requirements: You can use either Excel, VBA or MATLAB for this question. Ensure to clearly comment on each step and clearly indicate the final answer. Hint for Question 3: You need to simulate 2 sets of random daily returns for the two stocks with correlation of 0.3. To simulate correlated normal random variables, first simulate 2 sets of independent standard normal variables (with mean of zero and standard deviation of 1), 21 and 22. The daily return for the first stock will be x = mean(x) + stdev(x) + 2 . The daily return for the second stock will be y = mean(y) + stdev(y) * [218+22/(1 - p2)]. As per normal practice, use zero for the mean daily returns
