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 the stock-plus-put position on the expiration date of the option?

b. Now consider a portfolio consisting of a call option and a zero-coupon bond with the same expiration date as the option and with face value ( X D ). What is the value of this portfolio on the option expiration date? You should fi nd 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 cost of these portfolios, and you will derive the put-call parity relationship, Equation 16.3 .

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