Binomial Trees, Risk-Neutral Pricing, and American Style Options

Abstract

In the third chapter, binomial trees were introduced to price European style options in which the mean of the value of the moption at maturity was computed and then discounted to produce the price of the option (i.e., the option premium). Inputs for building the tree, U, D, P(U), and P(D), and the discount rate were provided for the exercise. In this chapter, the calculation of these pieces of the model will be revealed based on a model by Cox, Ross, and Rubinstein (1979). Further, risk-neutral pricing used within the binomial tree will be demonstrated to be a mathematical convenience and not a necessary condition for pricing options (i.e., there is no need for an assumption that all investors are risk neutral). Finally, the process for pricing an American style option with the binomial tree will be explained, which will allow for the pricing of real options in the next chapter.