You entered in a Forward contract some time ago on some stock S with a

delivery price of K$,$ to be delivered $6$ months from today. Today, you decide to long an OTC

European Put Option contract with a strike K to hedge some of the risk of this Forward

contract. To that end, you call the same counterparty that sold you the Forward contract,

who quotes you the following prices:

Instrument Price

Forward $$5\mathrm{.}5$

Put Option $$7\mathrm{.}7$

Call Option $$13\mathrm{.}5$

All the instruments above mature in $6$ months and have a delivery$/$strike price of K$.$

$($a$)$ What is the payoff of the total portfolio, that is$,$ the Forward you currently own plus

the Put Option you want to buy from your counterparty?

$($b$)$ Is this an arbitrage? Assume that, in case of default, there are no cash flows exchanged

between you and your counterparty.