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-Rubinstein 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-Ross-Rubinstein binomial option pricing model (CRR 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 Rubinstein.

The model is popular because it considers the underlying instrument over a period of time, instead of at just one point in time. It does this by using a lattice-based model, which 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 CRR 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). And, unlike the original Black-Scholes option pricing model, the CRR model has the ability to take into account the effect of dividends paid out by a stock during the life of an option. 

Cox-Ross-Rubinstein Method

The CRR model uses a risk-neutral valuation method. Its underlying principal affirms 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. Like the Black-Scholes model, the CRR model makes certain assumptions, including:

  • There is 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 CRR model employs an 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, creating a "binomial tree" – a graphic representation of possible values at different nodes.

The CRR 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-Rubinstein model is considered less complicated than the Black-Scholes model, you can use online calculators and trading platform-based analysis tools to determine option pricing values. Figure 6 shows an example of the Cox-Ross-Rubinstein model applied to an American-style options contract. The calculator produces both put and call values based on variables the user inputs.
 

Figure 6: The Cox-Ross-Rubinstein 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. Trading

    The Anatomy of Options

    Find out how you can use the "Greeks" to guide your options trading strategy and help balance your portfolio.
  3. Trading

    How to Build Valuation Models Like Black-Scholes

    Want to build a model like Black-Scholes? Here are the tips and guidelines.
  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

    The "True" Cost Of Stock Options

    Perhaps the real cost of employee stock options is already accounted for in the expense of buyback programs.
  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.
Frequently Asked Questions
  1. What Is a Holistic Marketing Strategy?

    Understand what holistic marketing is, and learn how the components of this strategy work when applied to different business ...
  2. What's the First Stock Warren Buffett Ever Bought?

    Find out about Warren Buffett's first experience in stock market trading. Learn some of the Berkshire Hathaway CEO's basic ...
  3. When Is a Put Option Considered to Be 'in the Money?'

    Learn about put options, how these financial derivatives work and when put options are considered to be in the money related ...
  4. What Are Some of the Top Hostile Takeovers of All-Time?

    Learn about some of the most noteworthy hostile takeovers in history, including the KKR acquisition of RJR Nabisco and the ...
Trading Center