The Binomial Model

History of the Binomial Pricing Model

The binomial pricing model is closely related to the Black Scholes model and its development stems from the mathematical formula. It was invented in 1979 by John Cox (a well-respected finance professor), Mark Rubinstein (a financial economist), and Stephen Ross (also a finance professor) originally to be used as a device to illustrate and explain to students of Cox how the Black Scholes model works.

However, unlike the Black Scholes model, it doesn't assume that an option is only exercised at the point of expiry. Because of this, it became apparent that it's more accurate when it came to calculating the values of American style options, whereas the Black Scholes method only really works for European style options. The binomial model became a widely used pricing model in its own right.

How the Binomial Pricing Model Works

The binomial pricing model is more complicated than the Black Scholes model and the calculations take longer, but it's considered to be generally more accurate. The Black Scholes model essentially states that an option has one correct value at the time of valuation and is used to calculate that theoretical value. The binomial model, however, calculates how the theoretical value of an option will change as time moves on and the price of the underlying security moves up or down. There are three steps involved.

The first step is the creation of what's known as a price tree, which contains a number of specific time points starting with the point of valuation and moving towards the point of expiration. Each of these points is referred to as a node, and the second step is to calculate theoretical valuations of the option for a number of different final nodes.

Each of the final nodes represent what the valuation of the option would be at the point of expiration given different prices of the underlying security. For example, you could have four final nodes that calculated the values of the option if the price of the underlying security had increased by 5%, increased by 10%, decreased by 5%, or decreased by 10%.

The final step of the process is calculating the theoretical values at each preceding node: working back from each of the final nodes towards the point of valuation. Once the process is completed, the price tree (or binomial tree) will show what the theoretical value of the option will be at various points in time, depending on how the price of the underlying security has changed.

The calculations involved are even more complex than the Black Scholes model and it's impractical for an options trader to carry them out; it's best to use a binomial model calculator. There are a number of these available on the internet, some of which are free and some of which are quite expensive. Some online brokers will provide a suitable tool to active customers at no cost though.

Using the Binomial Pricing Model

It is by no means vital for a trader to understand the binomial pricing model and use it for trading decisions. It does have its uses, and it can be beneficial for forecasting theoretical values of options based on how the underlying security moves in price and the amount of time that passes. However, it's not something that is absolutely essential and it's perfectly possible to be a successful options trader without using it.

For those traders that prefer to use a pricing model, the biggest advantage of the binomial model is that it's far more accurate in calculating theoretical values for American style options and taking early exercise into account. It's also more flexible for calculating how the theoretical values will change based on different variables.

The downside is that, as it involves more complex calculations, it's slower and not ideal for calculating the theoretical values of a large number of options for comparison purposes.

It certainly helps to have at least a basic understanding of options pricing models, because there may be a point when you want to use them. It isn't really a topic that you need to concern yourself with too much though, at least not until you are reasonably experienced with options trading and looking for ways to fine tune your trading tactics.