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 just at 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:

  • 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 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,  creating a "binomial tree" - a graphical 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. Investing

    Using Decision Trees In Finance

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

    The Anatomy of Options

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

    Exploring European Options

    The ability to exercise only on the expiration date is what sets these options apart.
  5. 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.
  6. Trading

    Getting Acquainted With Options Trading

    Learn more about stock options, including some basic terminology and the source of profits.
Frequently Asked Questions
  1. Why Do Most of My Mortgage Payments Start Out as Interest?

    Fear not: Over the life of the mortgage, the portions of interest to principal will change.
  2. What is the difference between secured and unsecured debts?

    The differences between secured and unsecured debt, and how banks buffer risks associated with each type of loan through ...
  3. How Many Times has Warren Buffett Been Married?

    Warren Buffett has been married twice in his life, but the circumstances surrounding the marriages were unconventional.
  4. What's the smallest number of shares of stock that I can buy?

    Many people would say the smallest number of shares an investor can purchase is one, but the real answer is not as straightforward. ...
Trading Center