Binomial options model
The Binomial options model provides a generalisable numerical method for the
valuation of options. It was first proposed by Cox, Ross and Rubinstein
The binomial 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.
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.
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.