Trinomial tree

The trinomial tree is a lattice based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar. It can also be shown that the approach is equivalent to the explicit finite difference method for option pricing.

Under the trinomial method, the underlying stock price is modeled as a recombining tree, where, at each node the price has three possible paths: an up, down and stable or middle path. These values are found by multiplying the value at the current node by the appropriate factor ${\displaystyle u\,}$, ${\displaystyle d\,}$ or ${\displaystyle m\,}$ where

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