9. Put-call parity and the value of a put option

Consider two portfolios A and B. At the expiration date, t, both portfolios have identical payoffs. Portfolio A consists of a put option and one share of stock. Portfolio B has a call option (with the same strike price and expiration date as the put option) and cash in the amount equal to the present value (PV) of the strike price discounted at the continuously compounded risk-free rate, which is XerRFtXerRFt. At expiration, the stock price is Ptt, and the value of this cash will equal the strike price, X.

Complete the equation for the putcall parity relationship.

....... +........ = ........... + .........

Now consider the stock of Grotesque Enterprises (GE) traded at the price P = $20 per share. A put option written on GEs stock has an exercise price of X = $25 and 18 months remaining until expiration. The risk-free rate is rRFRF = 8%. A call option written on GE has the same exercise price and expiration date as the put option. If the call option has a price of VCC = $6.50, then the price of the put option is ........ . (Note: Use 2.7183 as the approximate value of e.)