ABSTRACT
This chapter formally discusses derivative asset pricing within the multi-period binomial tree model. It begins by recalling the salient features of the standard T-period (recombining) binomial tree model on the space with two assets, namely, a risky stock and a risk-free asset, such as a bank account or zero-coupon bond. The chapter derives two methods for calculating derivative prices. The first method involves the use of a single-step recurrence formula, which is used to calculate the prices one by one recursively backward in time. The second method employs a multi-step pricing formulas. It allows us to calculate the derivative price at any intermediate date by averaging the values of the payoff function weighted by the risk-neutral probabilities of all the step paths. The risk-neutral pricing formula allows to compute the price of any path-dependent derivative. The early-exercise boundary, which separates the continuation and stopping domains, is a connected path in the binomial tree.
