Rebecca is interested in purchasing a European call on a hot new$$stock$,$ Up$,$ Inc. The call has a strike price of $$100\mathrm{.}00$ and expires in $91$ days. The current price of Up stock is $$115\mathrm{.}54,$ and the stock has a standard deviation of $36\%$ per year. The$$risk$-$free interest rate is $6\mathrm{.}61\%$ per year. Up stock pays no dividends. Use a$365-$day year.

a$.$ Using the$$Black$-$Scholes formula, compute the price of the call.

b$.$ Use$$put$-$call parity to compute the price of the put with the same strike and expiration date.