The Cox-Rubenstein (or Cox-Ross-Rubenstein) binomial option pricing model is a variation of the original Black-Scholes option pricing model. It was first proposed in 1979 by financial economists/engineers John Carrington Cox, Stephen Ross and Mark Edward Rubenstein. The model is popular because it considers the underlying instrument over a period of time, instead of just at one point in time, by using a lattice based model.

A lattice model takes into account expected changes in various parameters over an option's life, thereby producing a more accurate estimate of option prices than created by models that consider only one point in time. Because of this, the Cox-Ross-Rubenstein model is especially useful for analyzing American style options, which can be exercised at any time up to expiration (European style options can only be exercised upon expiration).

The Cox-Ross-Rubenstein model uses a risk-neutral valuation method. Its underlying principal purports that when determining option prices, it can be assumed that the world is risk neutral and that all individuals (and investors) are indifferent to risk. In a risk neutral environment, expected returns are equal to the risk-free rate of interest.

The Cox-Ross-Rubenstein model makes certain assumptions, including:

  • No possibility of arbitrage; a perfectly efficient market
  • At each time node, the underlying price can only take an up or a down move and never both simultaneously
The Cox-Ross-Rubenstein model employs and iterative structure that allows for the specification of nodes (points in time) between the current date and the option's expiration date. The model is able to provide a mathematical valuation of the option at each specified time, thereby creating a "binomial tree" - a graphical representation of possible values at different nodes.

The Cox-Ross-Rubenstein model is a two-state (or two-step) model in that it assumes the underlying price can only either increase (up) or decrease (down) with time until expiration. Valuation begins at each of the final nodes (at expiration) and iterations are performed backwards through the binomial tree up to the first node (date of valuation). In very basic terms, the model involves three steps:

  1. The creation of the binomial price tree
  2. Option value calculated at each final node
  3. Option value calculated at each preceding node
While the math behind the Cox-Ross-Rubenstein model is considered less complicated than the Black-Scholes model (but still outside the scope of this tutorial), traders can again make use of online calculators and trading platform-based analysis tools to determine option pricing values. Figure 6 shows an example of the Cox-Ross-Rubenstein model applied to an American-style options contract. The calculator produces both put and call values based on variables input by the user.

Cox-Ross-Rubenstein model applied to an American-style options contract.
Figure 6: The Cox-Ross-Rubenstein model applied to an American-style options contract, using the Options Industry Council\'s online pricing calculator.

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