Investment Theory and Risk Management, + Website

Option Payoffs and Put-Call Parity

Suppose you own a call option on a stock that you can exercise at time T at strike price K. If the spot price S is less than K, the call has zero value and will not be exercised. If, on the other hand, the spot prices exceeds K, then the call will have value equal to the difference S – K. The value of this option is depicted in Figure 16.1. As S exceeds K, the option value C exceeds zero. Thus, the call option is worth either zero because it goes unexercised if S < K or it has positive value equal to the difference S – K in the event S > K.

Figure 16.1 Call Value at Expiration

Put value is positive when the spot price is less than the strike price. In the limit, if the spot price were zero, then the value of the put would be equal to the strike price. As the spot price increases, then value declines and when S > K, the put has zero value and will not be exercised. Figure 16.2 depicts this relationship.

Figure 16.2 Put Value at Expiration

These two simple relationships were used by Robert Merton and Fischer Black and Myron Scholes to describe the capital structure of the firm. Those arguments are now standard fare in all corporate finance texts. Consider the example of a firm whose assets are financed by equity (shares) and debt (bonds). With no ...