T H E B I N O M I a L O P T I O N P R I C I N G M O D E L the Binomial Option Pricing Model

T he two major types of securities are stocks and bonds. A share of stock represents partial ownership of a company with an uncertain payoff which depends on the success of the specific business. Bonds, on the other hand, are loans which must be repaid except in cases of default; they can be issued either by governments or by business. Modern financial markets offer many other instruments besides stocks and bonds. Some of these instruments are called derivatives, since their price is derived from the values of other assets. The most popular example of a derivative is an option, which represents a contract allowing to one side to buy (in the case of a call option) or to sell (the case of a put option) a security on or before some specified maturity date in the future for a price which is set today. This prespecified price is called the exercise price or the strike price of the option. The two major classes of options are called European and American. A European option can be exercised only at maturity while an American option can be exercised at any time prior to maturity. Option pricing is topic of the current and the following article in this series. The price of an option is typically a non-linear function of the underlying asset (and some other variables, like interest rates, strike, etc.) The basis of any option pricing model is a description of the stochastic process followed by the underlying asset on which the option is written. In the Black-Scholes model, which will be discussed in the next article, the assumption is that the stock price is lognormally distributed (that the price follows a Wiener process with constant drift and variance). In this article we consider the case where the stock price follows a simple, stationary binomial process. At each moment in time, the price can go either up or down by a given percentage. When the stock price follows such a process and when there exists a risk-free asset, options written on the stock are easy to price. Furthermore, given appropriate limiting conditions, the binomial process converges to a lognormal price process and the binomial pricing formula converges to the Black-Scholes formula.