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Cox, Ross, Rubinstein Binomial Option Pricing Model

The Binomial Model for pricing American stock options was founded by Cox, Ross, and Rubenstein in 1979. Because of the graphical representation of the stock price and option price of the large number of intervals or steps, during the time period from valuation to expiration which are used in computing the option price, this model is categorized as a Lattice Model or Tree Model. With a probability defined by the volatility of the stock, the stock price will either move up or down at each step.

With the stock price on the valuation date, the graphical representation of the model starts at the left. The stock price can either branch up or down a calculated amount at the first interval. The stock price can either branch up or down at the second interval, from each of these two points, forming a lattice look. A larger structure is made throughout the time intervals up to the expiration date, while the branches continue.

The stock prices will increase at the risk-free interest rate minus the expected dividend yield, plus (for the up value) or minus (for the down value), is what is assumed by the model, and the price volatility is assumed for the stock.

The option values at each node are equal to the intrinsic value at that point, which is the expiration point, since the option is expired and has no extrinsic value at that point. What are then multiplied by their respective probabilities are the intrinsic values.

Calculating the option value at each point while taking into account any dividends paid along the way, the model then works backwards through each node. It has determined the present value of the option on the valuation date, using the risk-free interest rate, when it gets back to the left hand apex of the lattice. The option's fair values is the total of the present values of all the individual potential paths.

The option can only be exercised if the stock price increases above a specific level, which shows that this model can also accommodate Performance Based Options. What can also be dynamic over the term of the option are the inputs such as volatility, dividends, and interest rate, if there is information available on how those inputs should vary over the life of the option.

The Financial Account Standards Board requires that all companies determine and report the fair value of stock options compensating employees. The FASB Statement NO. 123® allows companies to use any valuation model that is based on established principles of financial economic theory and reflects all substantive characteristics of the options. The option pricing model uses all of the factors that are recommended by the Financial Accounting Standards Board (FASB), including the exercise price of the option, the expected term of the option, the current expected dividends on the underlying share, and the risk-free interest rate.

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