The binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein (1979). Essentially, the model uses a “discrete-time” model of the varying price over time of the underlying financial instrument.An options valuation method developed by Cox, et al, in 1979. The binomial option pricing model uses an iterative procedure, allowing for the specification of nodes, or points in time, during the time span between the valuation date and the option’s expiration date.
The Binomial options pricing model approach is widely used as it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time. Being relatively simple, the model is readily implementable in computer software (including a spreadsheet).
The model reduces possibilities of price changes, removes the possibility for arbitrage, assumes a perfectly efficient market, and shortens the duration of the option. Under these simplifications, it is able to provide a mathematical valuation of the option at each point in time specified.
Pricing Model
The binomial model takes a risk-neutral approach to valuation. It assumes that underlying security prices can only either increase or decrease with time until the option expires worthless. A simplified example of a binomial tree might look something like this:
Binomial Option Pricing Model
Due to its simple and iterative structure, the model presents certain unique advantages. For example, since it provides a stream of valuations for a derivative for each node in a span of time, it is useful for valuing derivatives such as American options which allow the owner to exercise the option at any point in time until expiration (unlike European options which are exercisable only at expiration). The model is also somewhat simple mathematically when compared to counterparts such as the Black-Scholes model, and is therefore relatively easy to build and implement with a computer spreadsheet.