Chapter 20. Binomial Option Pricing
In Chapter 19: Options and Option Portfolios, we saw that the Black-Scholes-Merton (BSM) equations can be used to calculate prices for European options. They cannot, however, be used to price most American options or many other types of options. In this chapter, I discuss a versatile and popular technique for pricing not just any type of option, but any type of derivative security. It involves creating binomial trees and using them in conjunction with the risk-neutral valuation method. I will discuss only what you need to know to develop the models in this chapter. My review parallels the discussions in Options, Futures, and Other Derivatives by John C. Hull (6th edition), and you can refer to that book or any other books on derivatives for additional details.
Review of Theory and Concepts
It is generally easier to understand binomial trees and their uses by working through some examples, and that is what we will do when we build the models later in the chapter. If you are new to binomial trees and do not fully understand everything in the following theoretical discussions, read through them once and go on to the modeling section. Things will become clearer once you start working on the models.
A binomial tree represents the different possible paths that the price of a stock or other security can follow over time. Binomial trees have to be built following certain rules so that the paths they generate are realistic.
Let us assume that ...