Binomial options model
The Binomial options valuation model provides a generalisable numerical method for the valuation of options given a price change in the option's underlying instrument. This price change is modelled via the Binomial pricing model, which is a “discrete-time” model of the varying price over time of financial instruments. This methodology was first proposed by Cox, Ross and Rubinstein (1979).
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2 Relationship with Black-Scholes 3 See also 4 External links and References |
Methodology
The binomial pricing model uses a "discrete-time framework" to trace the evolution of the option's key underlying variable via a binomial lattice (tree) for a given number of time steps between t = 0 and option expiration. The resultant evolution then forms the basis for the option valuation which is as follows: Given the option style, the value of the option at any node in the lattice is determined using the risk neutrality assumption for the price of the underlying at that node, and the value of the option at the two later nodes (or the exercise value at a final node). The process is iterative, starting at each final node, and then working backwards through the tree to t = 0, where the calculated value is the value of the option in question. The methodology is best illustrated via example; link here for an online, graphical Binomial Tree Option Calculator.
Relationship with Black-Scholes
Similar assumptions underpin both the binomial model and the Black-Scholes model, and the binomial model thus provides a discrete time approximation to the continuous process underlying the Black-Scholes model. In fact, for European options, the binomial model value converges on the Black-Scholes formula value as the number of time steps increases.
See also
External links and References
