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 , 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 . Calculate a 10 -day $99 \% \mathrm{VaR}$ : (a) Using only deltas (b) Using the partial simulation approach (c) Using the full simulation approach.

   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 , 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 . Calculate a 10 -day $99 \% \mathrm{VaR}$ :
(a) Using only deltas
(b) Using the partial simulation approach
(c) Using the full simulation approach.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 22, Problem 20

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Step 1

For the call option: The delta for a call option is given by the formula: $\Delta_{\text{call}} = e^{-rT}N(d_1)$ where $r$ is the risk-free rate, $T$ is the time to maturity, and $N(d_1)$ is the cumulative standard normal distribution of the variable Show more…

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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 , 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 . Calculate a 10 -day $99 \% \mathrm{VaR}$ : (a) Using only deltas (b) Using the partial simulation approach (c) Using the full simulation approach.

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