QUESTION $3$

Required:

a$)$ Critically evaluate the terminal value of the following portfolio: a newly entered$-$into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up$.$ Prove that the European put option has the same value as a European call option with the same strike price and maturity. Illustrate your answer with figure.

b$)$ Calls were traded on exchanges before puts. During the period of time when calls were traded but puts were not traded, how would you create a European put option on a non$-$dividend paying stock synthetically?

c$)$ Critically explain why the arguments leading to put$-$call parity for European options cannot be used to give a similar result for American options.