Option Pricing and Market Data

Ross (1987) has noted that option pricing theory is “the most successful theory not only in finance, but in all of economics.” A call (put) option gives the holder the right to buy (sell) the underlying asset (e.g., stock) by a certain date, known as the expiration date or maturity, at a certain price, which is called the strike price. “European” options can be exercised only on the expiration date, whereas “American” options can be exercised at any time up to the expiration date. The celebrated theory of Black and Scholes (1973) yields explicit formulas for the prices of European call and put options. Merton (1973) extended the Black-Scholes theory to American options. Optimal exercise of the option has been shown to occur when the asset price exceeds or falls below an exercise boundary for a call or put option, respectively. There are no closed-form solutions for the exercise boundary and American option price, but numerical methods and approximations are available, as described in Section 8.1. The Black-Scholes-Merton theory for pricing and hedging options is of fundamental importance in the development of financial derivatives and provides the foundation for financial engineering. A derivative is a financial instrument having a value derived from or contingent on the values of more basic underlying variables. In particular, a stock option is a derivative whose value is dependent on the price of the stock. In recent years, credit derivatives and path-dependent options have become popular, and there are emerging markets in weather, energy, and insurance derivatives; see Chapters 21–23 of Hull (2006).