(a) Explain the similarities and differences between being the short party of a forward contract and being the holder of an American put option contract. [ 6 marks ] Suppose St is the price of a company's share at time t. Let at time t, ct be the price of a European call option contract and pt be the price of a European put option contract on the share with the same strike price K and maturity date T. The continuously compounded constant risk-free rate of interest is r per annum. Consider two times u and v such that t < u < v < T. Let a single dividend payment of D per share is to be paid at time u and a single custodian fee of E per share has to be paid at time v. (A custodian is a financial institution that holds customers' shares for safekeeping to prevent them from being stolen or lost.)

(b) Show that: ct + K er(T t) + D er(ut) = pt + St + E er(vt) . [ 6 marks ]

(c) Discuss the impact of dividend payments and custodian fees on European call and put option prices. [ 4 marks ] [ Total: 16 marks ]