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Cox, Ross, Rubinstein Binomial Option Pricing Model

Cox, Ross, and Rubinstein introduced the Binomial Model for pricing American stock options in 1979. This model is categorized as a Lattice Model or Tree Model because of the graphical representation of the stock price and option price over the large number of intervals or steps, during the time period from valuation to expiration, which are used in computing the option price. At each step, the stock price will either move up, or down, with a probability defined by the volatility of the stock.

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

The model assumes that 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) the price volatility assumed for the stock.

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

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

This model can also accomodate Performance Based Options, where the option can only be exercised if the stock price increases above a specific level. The inputs such as volatility, dividends, and interest rate, can also be dyanamic over the term of the option, if there is information available on how those inputs should vary over the life of the option.

The Financial Accounting Standards Board requires all companies to determine and report the fair value of stock options they use to compensate employees. FASB Statement No. 123(R) 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. This 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. This model can also utilize information such as the early exercise behavior of employees, if that information is available.

We have several products and services to meet your specific needs for option valuation.

We provide Company Stock Option Services for companies that want to ensure proper valuation of the options they grant so that they can meet the new requirements of the Financial Accounting Standards Board (FASB). We have low-priced services to determine the fair value for your options and we also provide services to track your options.

We provide Employee Stock Option Services for employees of companies who own options and would like to determine what their specific options are really worth now and predict their value in the future. Our services also help employees to exercise their options at the best time to maximize their wealth.

For option traders or companies who want a stand-alone program for option valuation, we market option pricing software, which can determine fair value for options. This excellent program can also help option traders maximize their profits since it can calculate the probability of success with your trades and help you select winning strategies.





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