binomial

A model used to determine the fair value of options uses an iterative procedure, allowing for the specification of nodes during the time between the valuation date and the option’s expiration date. At each node, the model assumes the underlying asset can move to only one of two possible prices. This creates a binomial tree representing multiple potential paths the underlying asset’s price could follow. A simple example considers a call option: At each node, its value is calculated as the difference between the underlying asset price and the strike price, or zero if the difference is negative. This method applies a risk-neutral valuation principle, assuming the underlying asset’s price moves in discrete up and down steps. The model then works backward from the expiration date to the present, computing option values at each previous node.

This approach offers computational advantages, particularly with American-style options, which can be exercised before their expiration date. It provides a clear and understandable framework for valuing options, even with complex features. Historically, before widespread computational power, this methodology served as a crucial tool for option pricing. Its relative simplicity compared to more complex models made it more accessible and computationally feasible. Though more sophisticated models exist, this one continues to be useful for its pedagogical value in illustrating core option pricing principles.

Read more