A stock is trading at S $=50.$ There are one$-$month European calls and puts on the stock

with a strike of $50.$ The call is trading at a price of CE $=3.$ Assume that the one$-$month

rate of interest $($annualized$)$ is $2\%$ and that no dividends are expected on the stock over

the next month.

$($a$)$ What should be the arbitrage$-$free price of the put?

$($b$)$ Suppose the put is trading at a price of PE $=2\mathrm{.}70.$ Are there any arbitrage opportunities?