The trinomial tree is a clear extension of the binomial tree where the extra node adds an extra degree of freedom. The derivation of the basic trinomial tree is based on moment matching as well as a stability relation to preclude negative probabilities. The trinomial tree has a clear connection to a triangular slice of the rectangular explicit finite difference grid.
The geometric Brownian motion stochastic differential equation
can be transformed via and Ito's lemma into the normally distributed
where is the continuously compounded return drift factor. Similarly, the risk-neutral evolution of the price change
with a dividend yield can be transformed into the logarithm of the price change with a log-normal drift of . A derivative based on the log price of the asset follows the differential equation
In order to ...