# Binomial Option Pricing

12 Pages Posted: 12 Jun 2009

See all articles by Robert M. Conroy

## Robert M. Conroy

University of Virginia - Darden School of Business

### Abstract

This note is designed to introduce the binomial option-pricing model. It covers the basic concepts using a one-period model and then provides an example of a two-period model. The note focuses on a conceptual approach to binomial option pricing rather than formulas.

Excerpt

UVA-F-0943

BINOMIAL OPTION PRICING

Binomial option pricing is a simple but powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes and other complex option-pricing models that require solutions to stochastic differential equations, the binomial option-pricing model (two-state option-pricing model) is mathematically simple. It is based on the assumption of no arbitrage.

The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of return and no investment opportunities exist that require zero dollars of investment but yield positive returns. It is the activity of many individuals operating within the context of financial markets that, in fact, upholds these conditions. The activities of arbitrageurs or speculators are often maligned in the media, but their activities ensure that our financial markets work. They ensure that financial assets such as options are priced within a narrow tolerance of their theoretical values.

Binomial Option-Pricing Model

Assume that we have a share of stock whose current price is \$ 100/share. During the next month, the price of the stock is either going to go up to \$ 110 (up state) or go down to \$ 90 (down state). No other outcomes are possible over the next month for this stock's price.

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Keywords: model evaluation, option pricing

Suggested Citation

Conroy, Robert M., Binomial Option Pricing. Available at SSRN: https://ssrn.com/abstract=1417864 or http://dx.doi.org/10.2139/ssrn.1417864