Introduction

The module on “Binomial Trees” is an essential component of understanding option pricing models in finance. This chapter serves as a gateway to this topic by providing an overview of option pricing models, highlighting the importance of binomial trees, and outlining the objectives of this module.

Overview of Option Pricing Models

Option pricing models are mathematical tools used to determine the fair value of financial derivatives, particularly options. These models are crucial for investors and financial analysts to make informed decisions about trading options. Option pricing models aim to answer questions like, “What is the fair market price for this option?” and “How do various factors affect option prices?”

Importance of Binomial Trees

Among the various option pricing models, binomial trees hold a unique place due to their simplicity and versatility. Binomial trees provide a clear and intuitive way to value options under different scenarios. They are particularly useful for American options, which can be exercised at any time before expiration. Understanding binomial trees is fundamental for comprehending more complex models like the Black-Scholes-Merton model.

Objectives of the Module

In this module, we will explore binomial trees in detail, with the following objectives in mind:

• Calculate the value of American and European call or put options using both one-step and two-step binomial models.

• Describe how volatility, a critical factor in option pricing, is incorporated into the binomial model.

• Understand how the calculated option values converge as more time periods are added to the binomial tree.

• Define and calculate delta, a measure of an option’s sensitivity to changes in the underlying asset’s price.

• Explore how the binomial model can be adapted to price options on various assets, including stocks with dividends, stock indices, currencies, and futures.