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Any model that incorporates a binomial tree, also called a binomial lattice. A binomial model describes the evolution of a random variable over a series of time steps, assigning given probabilities to a rise or fall in the variable.
After the initial rise or fall, the next two branches will each have two possible outcomes, so the process will continue, building a ‘tree’ over time. The process is usually specified, so that an upward movement followed by a downward movement results in the same price, so the branches recombine.
Binomial trees are of interest because they can be used to deal with American-style features; the early-exercise condition can be tested at each point in the tree.