Suppose the risk$-$free interest rate is $5\%$ per annum with continuous compounding. The $3-$month forward price for the XYZ stock is $$100.$ Consider

the following premiums for the XYZ options with $3$ months to expiration:

Strike Call Put

$$80$ $$33$ $$10$

Assume that the stock pays no dividends and it costs nothing to enter into

the forward contract.

$($i$)$ Is put$-$call parity violated? Justify your answer.

$($ii$)$ Construct a portfolio $($strategy$)$ that generates an arbitrage.

$($iii$)$ Calculate the $($riskless$)$ profit guaranteed by the portfolio in part $($ii$)$

at end of $3$ months.