9. In this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $ D per share at the expiration date of the option.

a. What is the value of a stock-plus-put position on the expiration date of the option?

b. Now consider a portfolio comprising a call option and a zero-coupon bond with the same maturity date as the option and with face value ( X + D ). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio regardless of the stock price.

c. What is the cost of establishing the two portfolios in parts ( a ) and ( b )? Equate the costs of these portfolios, and you will derive the put-call parity relationship, Equation 20.2 .