\"A bank has written a call option on one stock and a put option on another stoc
ID: 2739763 • Letter: #
Question
"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 9 months. For the second option the stock price is 20, the strike price is 19, and the volatility is 25% 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 price returns is 0.4."
What's the expected returns and standard deviation of the portfolio?
Explanation / Answer
The daily volatility of two stocks are = 0.28 / 252 = 0.0176
= 0.25 / 252 = 0.0157
= 29.45 * 29.45 * 0.0176 * 0.0176 + 568* 568 * 0.0157 * 0.0157 – 29.45 * 0.0176 * 568 * 0.0157
= 0.2396
Standard deviation is therefore = 0.4895 and the 10 days 99% Var is 2.33
2.33 10* 0.4895 = 361.
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