Question $3$: Implied Volatility and Put$-$Call Parity $(3/10).$

Suppose S $=100$ and there are both a $9-$month European call and a $9-$month European

put with K $=100.$ The continuously compounded risk$-$free rate is $5\%,$ and there are no

payouts.

$($i$)$ The call currently trades at a price of $14\mathrm{.}087.$ What is the Black$-$Scholes implied

volatility?

$($ii$)$ The put trades at an implied volatility of $36\mathrm{.}85\%.$ Is there an arbitrage opportunity

here? If so$,$ how would you take advantage of it and what are the cash flows?Question $3$: Implied Volatility and Put$-$Call Parity $(3/10).$

Suppose $S=100$ and there are both a $9-$month European call and a $9-$month European

put with $K=100.$ The continuously compounded risk$-$free rate is $5\%,$ and there are no

payouts.

$($i$)$ The call currently trades at a price of $14\mathrm{.}087.$ What is the Black$-$Scholes implied

volatility?

$($ii$)$ The put trades at an implied volatility of $36\mathrm{.}85\%.$ Is there an arbitrage opportunity

here? If so$,$ how would you take advantage of it and what are the cash flows?