A trinomial tree allows three next-step states. For the explicit log-price scheme for local-volatility pricing these are , with the displayed weights. They sum to one; if nonnegative they are transition probabilities and make backward pricing a conditional average. Their first two increment moments are and , matching the diffusion to first order in the time step. Coefficients can depend on the node, so the tree need not have constant transition probabilities.
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A trinomial tree is a type of mathematical model used in financial mathematics to evaluate options and other derivative securities. It extends the binomial tree model by allowing for three possible outcomes at each step in the model, rather than just two. ### Key Features of a Trinomial Tree: 1. **Multiple Outcomes**: At each node (point in time), the underlying asset price can move in three possible directions: up, down, or stay the same.