Option Basics -- IX

Put call parity

Anup Menon

ONE of the important properties of options prices is that at a particular point in time the value of a European call option with a particular exercise date and exercise price can be obtained from the value of a put with the same exercise date and strike price.

This relationship is known as put call parity. However the relationship is strict only in the case of European options. What is important for traders is that if there is a violation, then there is an arbitrage opportunity. The concept is better understood with an example.

For instance, assume that there are two portfolios. One contains a call option and an amount in cash which is equal to the discounted value of the exercise price. The other portfolio consists of one European put option and one share. Now the sum of the call price plus the cash in portfolio A should be equal to the sum of the put price and the Stock price in portfolio B. Now assume that the computations indicate that the values of portfolio A and B are not equal. Then what will be strategy to be adopted.

If the value of portfolio B is more than portfolio A, then it indicates that portfolio B is overvalued. Then what would be the strategy adopted. The investor would have to buy the securities in portfolio A and sell the securities in portfolio B. This means that the investor has to buy the call and short the put and the stock. This strategy would generate a positive cash flow upfront for the investor. This cash when invested at the risk-free rate for the time period is greater than the exercise price of the security. Since both stocks have the same exercise price, either way the stock moves, the investor gets to buy the stock at the exercise price. Hence the net profit made by the investor would be the difference between the value of the initial cash inflow and the exercise price of the contracts.