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 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:
- The creation of the binomial price tree
- Option value calculated at each final node
- Option value calculated at each preceding node
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
TradingFind out how to carve your way into this valuation model niche.
InvestingThese decision-making tools play an integral role in corporate finance and economic forecasting.
TradingFind out how you can use the "Greeks" to guide your options trading strategy and help balance your portfolio.
TradingMathematical 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. ...
InvestingBinomial option pricing model, based on risk neutral valuation, offers a unique alternative to Black-Scholes. Here are detailed examples with calculations using Binomial model and explanation ...
TradingWant to build a model like Black-Scholes? Here are the tips and guidelines for developing a framework with the example of the Black-Scholes model.
TradingPerhaps the real cost of employee stock options is already accounted for in the expense of buyback programs.
InvestingThe 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 ...
InvestingLearn about stock options and the "volatility surface," and discover why it is an important concept in stock options pricing and trading.
Small BusinessBusiness model is the term for a company’s plan as to how it will earn revenue.