1. Options Pricing: Introduction
  2. Options Pricing: A Review Of Basic Terms
  3. Options Pricing: The Basics Of Pricing
  4. Options Pricing: Intrinsic Value And Time Value
  5. Options Pricing: Factors That Influence Option Price
  6. Options Pricing: Distinguishing Between Option Premiums And Theoretical Value
  7. Options Pricing: Modeling
  8. Options Pricing: Black-Scholes Model
  9. Options Pricing: Cox-Rubenstein Binomial Option Pricing Model
  10. Options Pricing: Put/Call Parity
  11. Options Pricing: Profit And Loss Diagrams
  12. Options Pricing: The Greeks
  13. Options Pricing: Conclusion

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.


Options Pricing: Put/Call Parity

Related Articles
  1. Trading

    Breaking Down The Binomial Model To Value An Option

    Find out how to carve your way into this valuation model niche.
  2. Investing

    Using Decision Trees In Finance

    These decision-making tools play an integral role in corporate finance and economic forecasting.
  3. Trading

    Circumvent Limitations of Black-Scholes Model

    Mathematical or quantitative model-based trading continues to gain momentum, despite major failures like the financial crisis of 2008-09, which was attributed to the flawed use of trading models. ...
  4. Investing

    Understanding the Black-Scholes Model

    The Black-Scholes model is a mathematical model of a financial market. From it, the Black-Scholes formula was derived. The introduction of the formula in 1973 by three economists led to rapid ...
  5. Trading

    Exploring European Options

    The ability to exercise only on the expiration date is what sets these options apart.
  6. Investing

    The Volatility Surface Explained

    Learn about stock options and the "volatility surface," and discover why it is an important concept in stock options pricing and trading.
  7. Small Business

    What is a Business Model?

    Business model is the term for a company’s plan as to how it will earn revenue.
  8. Trading

    Options Pricing

    Options are valued in a variety of different ways. Learn about how options are priced with this tutorial.
Frequently Asked Questions
  1. What is the difference between yield and return?

    While both terms are often used to describe the performance of an investment, yield and return are not one and the same ...
  2. What are the Differences Among a Real Estate Agent, a broker and a Realtor?

    Learn how agents, realtors, and brokers are often considered the same, but in reality, these real estate positions have different ...
  3. What is the difference between amortization and depreciation?

    Because very few assets last forever, one of the main principles of accrual accounting requires that an asset's cost be proportionally ...
  4. Which is better, a fixed or variable rate loan?

    A variable interest rate loan is a loan in which the interest rate charged on the outstanding balance varies as market interest ...
Trading Center