
Binomial tree

Also called a binomial lattice. A discrete time model for describing the evolution of a random variable that is permitted to rise or fall with given probabilities. After the initial rise, two branches Will each have two possible outcomes and so the process Will continue. The process is usually specified so that an upward movement followed by a downward movement results in the same price, so that the branches recombine. If the branches do not recombine it is known as a bushy, or exploded, tree. The size of the movements and the probabilities are chosen so that the discrete Binomial model tends to the normal Distribution assumed in Option models as the number of discrete steps is increased. Options can be evaluated by discounting the terminal payoff back through the tree using the determined probabilities. Interest in binomial trees arises from their ability to deal with Americanstyle features and to price Interest rate options. For example, Americanstyle options can readily be priced because the early Exercise condition can be tested at each point in the tree.

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