$(7\mathrm{.}5$points$)$ Suppose there are both call and put options available on the number of

points Shaquille O'Neal will score in his next game. For example, a call option with

an exercise price of $32$ pays off max $S-32,0,$ where $S$ is the number of points Shaq has

recorded by the end of the game. Thus if he scores $35$ points, call holders receive $$3$

for each call. If he scores less than $32$ points, call holders receive nothing. Assume

that there is no way to actually buy a position in the underlying asset, which pays off

the number of points scored by Shaq.

a$)$ Show, using an arbitrage table, how you can use puts, calls and zero$-$coupon

bonds to construct a synthetic security which pays off the number of points Shaq

scores in the game.

b$)$ Currently, the price of a call is $S8$ and the price of a put is $S3($both with an

exercise price of $32).$ Assuming that the game is being played tomorrow $($no

discounting necessary$),$ determine the fair value of the synthetic security which

pays of the number of points Shaq scores in the game.

Right before the game someone starts to make a market in the underlying

security. At this time, the price of the call equals $$7,$ the put is priced at $$4,$ and

the underlying security is priced at $$34.($Again$,$ assume that the exercise prices

for the call and the put are the same: $32)$

c$)$ Is there an arbitrage opportunity? If yes, show exactly how you would exploit

the arbitrage opportunity.