A $4-$month European $60-$strike call on a dividend$-$paying stock is currently selling for $6.$ The cur$-$

rent stock price is $60$ and a dividend of $0\mathrm{.}5$ is expected in $2$ months. The continuously compounded

risk$-$free interest rate is $8\%.$

$($a$)$ Calculate the non$-$arbitrage price of a $4-$month European $60-$strike put on the stock.

$($b$)$ Construct an arbitrage portfolio if the put option price is $5,$ assuming an investor can lend

or borrow at the risk$-$free interest rate. Generate the payoff table to verify the constructed

portfolio is an arbitrage.