Please solve the following questions.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 $500,$

the strike price is $527,$ the volatility is $29\%$ per annum, and the time to maturity is $9$ months. For the second option the

stock price is $300,$ the strike price is $276,$ the volatility is $20\%$ per annum, and the time to maturity is $10$ months. Neither

stock pays a dividend, the risk$-$free rate is $9\%$ per annum, and the correlation between stock price returns is $0\mathrm{.}2.$

Use the linear approximation to answer the followings.

$(1)$ The standard deviation of the change in the call option in one day is

$(2)$ The standard deviation of the change in the put option in one day is

$(3)$ The $5-$day $90\%$ VaR for the portfolio of the bank is