QUESTION $5$

$1$ points

The following prices are available for call and put options on a stock priced at $$50.$ The risk$-$free rate is $6$ percent and the volatility is $0\mathrm{.}35.$ The March options have $90$ days remaining and the June options have $180$ days remaining. The Black$-$Scholes model was used to obtain the prices.

$\backslash$table$[[,$Calls,Puts$],[$Strike$,$March,June,March,June$],[45,6\mathrm{.}84,8\mathrm{.}41,1\mathrm{.}18,2\mathrm{.}09],[50,3\mathrm{.}82,5\mathrm{.}58,3\mathrm{.}08,4\mathrm{.}13],[55,1\mathrm{.}89,3\mathrm{.}54,6\mathrm{.}08,6\mathrm{.}93]]$

Assume that each transaction consists of one contract $($for $100$ shares$)$ unless otherwise indicated. Consider a bull money spread using the March $45/50$ calls.

What is the profit if the stock price at expiration is $$47?$

a$.$ $$302$

b$.$ none of the above

c$.$ $$102$

d$.$ $$500$

e$.$ $$398$