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5.1 Overview

One limitation of the one-period and two-period binomial models is that the set of possible terminal stock values is quite small. This limitation is overcome in a multi-period model of stock price movements. For example, suppose there are five hours remaining in a trading day and one period equals one hour. At the end of the day, the multi-period binomial model would allow for 32 (25) possible end-of-day prices. If a period equals one minute, we have 2300 possible ending values.

We extend the two-period binomial option pricing model to n-periods in topic 5.2, Binomial Option Pricing: N-Periods. Appendix C Chapter 5 Technical Topic: Limiting Results, provides the formal derivation of this n- period model, Binomial Option Pricing: N-Period Derivation.

The limiting behavior of this approach, as periods become smaller and smaller, is discussed in topic 5.4, called Binomial Option Pricing: Limiting Results. The n-period model converges in the limit to the Black-Scholes option pricing model. One advantage of the binomial approach is that not only does it accommodate a wide range of option pricing problems, but also it provides an interpretation of the Black-Scholes pricing model.

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