$(6\%)$ a$.$ Use the Black$-$Scholes formula to find the value of a put option on the following

stock:

Time to maturity $=12$ months

Standard deviation $20\%$ per year

Exercise price $=$ $$100$

Stock price $=$ $$100$

Interest rate $=5\%$

Annual dividend yield $=0\%$

$(7\%)$ b$.$ Suppose one can find a $$11\mathrm{.}5$ call option on the stock in part $($a$)$ with the same

exercise price and maturity as the call option. Would an arbitrage opportunity exist?

If so$,$ what would be the arbitrage strategy? $($You need to specify long and short of

these positions as well as initial and ending cash flows.$)$