On the Irrelevance of Expected Stock Returns in the Pricing of Options in the Binomial Model: A Pedagogical Note

Abstract

The option pricing theory is now either a standard or a main part of many financial courses on both intermediate and advanced levels. All the textbooks that include the option pricing theory present a detailed treatment of the binomial model. However, the binomial model, although quite simple and intuitive in appearance, is rather tricky when it comes to its practical implementations and applications. In fact, it is amazing that the students often get totally confused when it finally comes to the issue of the choice of the parameters of the binomial model. The reason for all this confusion lies in the fact that all the textbooks emphasize the irrelevance of the binomial option price from the probabilities of upward and downward movements in the stock price in the objective world, instead of emphasizing the irrelevance of the option price from the expected returns of the underlying stock. Consequently, the main purpose of this paper is to demonstrate the irrelevance of expected stock returns in the pricing of options in the binomial model.

Keywords: option pricing, binomial model

JEL Classification: G13, A23