Consider an American put option on a non$-$dividend paying stock. The stock is currently

priced at $$60$ and the put is priced at $$3.$ The option has $6$ months to expiration and a strike

of $$66.$ The risk$-$free rate is $8\%$ p$.$a$.$ continuously compounded and the market expects it to

rise to $9\%$ p$.$a over the coming week. Which of the following statements is true?

$($a$)$ An American put should never be exercised early.

$($b$)$ An arbitrageur can buy the put and the stock, and exercise immediately, earning a

profit of $$3.$

$($c$)$ An arbitrageur can buy the put and the stock and exercise immediately, earning a

profit of $$2\mathrm{.}8824.$

$($d$)$ An arbitrageur can sell the put and stock and buy bonds, immediately earning a

profit of $$2\mathrm{.}8824.$

$($e$)$ None of the above.