Options Pricing: CoxRubenstein Binomial Option Pricing Model
The CoxRubenstein (or CoxRossRubenstein) binomial option pricing model is a variation of the original BlackScholes 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 CoxRossRubenstein 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 CoxRossRubenstein model uses a riskneutral 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 riskfree rate of interest.
The CoxRossRubenstein 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 CoxRossRubenstein model is a twostate (or twostep) 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 CoxRossRubenstein model applied to an Americanstyle options contract, using the Options Industry Council\'s online pricing calculator. 

Theta
A measure of the rate of decline in the value of an option due ... 
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