As a chief strategy officer at an investment bank Thanks For Your Hard Work At HPS INC, you are now asked by the CEO to create a product consisting of : 1) a long forward contract on an underlying asset and 2) a long European put option on the same asset with the same maturity as the forward contract and a strike price that is equal to the forward price. You feel that the CEO is going crazy and you think such a complicated product is no more than a long call option on the asset. Denote the maturity for the forward contract and the put option as T, denote the strike price and the forward price as X, and denote the price of the asset at T as ST .

a. [4 points] Write down the payoff of the product at time T (consisting of the long forward contract and the long European put)

b. [6 points] prove mathematically that the payoff in part a is exactly the same as the payoff of a long call option on the same underlying asset.

c. [5 points] Instead of using a mathematical proof in part b, illustrate with the payoff diagrams that such a complicated product is exactly the same as a long call option on the same underlying asset.

d. [5 points] After the CEO sees your amazing proof and diagrams, she shouts out, Then a long forward contract is equivalent to a long position in a European call and a short position in a European put! Is her statement correct? Prove mathematically why that is correct or incorrect, possibly using your results in part a, b or c.