Options Pricing: Cox-Rubenstein Binomial Option Pricing Model
  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

Options Pricing: Cox-Rubenstein Binomial Option Pricing Model

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

  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
RELATED TERMS
  1. Binomial Option Pricing Model

    An options valuation method developed by Cox, et al, in 1979. ...
  2. Binomial Tree

    A graphical representation of possible intrinsic values that ...
  3. Lattice-Based Model

    An option pricing model that involves the construction of a binomial ...
  4. Option Pricing Theory

    Any model- or theory-based approach for calculating the fair ...
  5. Black's Model

    A variation of the popular Black-Scholes options pricing model ...
  6. Model Risk

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RELATED FAQS
  1. What is the average return on equity for a company in the electronics sector?

    Learn about the Black-Scholes option pricing model and the binomial options model, and understand the advantages of the binomial ... Read Answer >>
  2. How is implied volatility for options impacted by a bearish market?

    Learn why implied volatility for option prices increases during bear markets, and learn about the different models for pricing ... Read Answer >>
  3. When holding an option through expiration date, are you automatically paid any profits, ...

    Holding an option through the expiration date without selling does not automatically guarantee you profits, but it might ... Read Answer >>
  4. What technical skills must one possess to trade options?

    Learn about the technical skills required to trade options and how mathematical and computer science skills give you a better ... Read Answer >>
  5. How are call options priced?

    Learn how aspects of an underlying security such as stock price and potential for fluctuations in that price, affect the ... Read Answer >>
  6. How do you tell whether an option is American or European style?

    As a quick recap, American-style options are options that can be exercised at the strike price anytime before or on the date ... Read Answer >>

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