models that relate a number of variables and yield a theoretical price that is useful in judging whether an option or other derivative is fairly priced by the market or is overvalued or undervalued. The best-known and most widely adapted model is the basic black-scholes option pricing model, developed by Fischer Black and Myron Scholes in the 1960s for options on stocks and modified in the 1970s for options on futures. Others are the Cox-Ross Pricing Model and the Bi Nomal Option Pricing Model. Black-Scholes uses the following five variables: 1. time remaining to expiration; 2. market price of the underlying stock or futures contract; 3. the exercise or strike price of the option; 4. carrying charges (interest rate, dividends for stocks); and 5. the volatility of the underlying stock or contract. Among other benefits, the Black-Scholes formula calculates the hedge ratio or delta, the theoretical percentage change in an option price caused by each one-point change in the price of the underlying stock or future. The delta thus provides a comparative valuation between the options price movement and the underlying asset over a one point move in the asset, assuming no change in time to expiration. A move of more than one point or a change in time, however, causes a change in the delta. A change in the delta, called a gamma, is measured by another model called the Gamma Pricing Model. The Vega Pricing Model measures the change in the option price caused by a change in volatility. The Theta Pricing Model measures the change in the option price caused by a change in the time value.
Derivative pricing is highly complex and has been made easier by available computer programs and Internet services.
