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.
P = C – S0 + PV(X) + PV (dividends)