Why do interest rate models use trinomial trees instead of binomial?

Question

AcadiFi · Accepted Answer

Trinomial trees add a third branch (up, middle, down) at each node, giving more flexibility for matching mean-reverting dynamics common in interest rates. With Hull-White, the short rate reverts to a long-term mean at speed a, and a binomial tree struggles to fit both the drift and volatility of r(t). Trinomials let you freeze the spatial grid (fixed rate levels) and adjust branching probabilities to match conditional expected change. For example, with a = 0.12 and volatility 1.4%, at high rate nodes you'd use down-biased branching (probabilities favor the lower middle node) to mimic pull-back, and at low nodes up-biased branching. Binomial trees can't do this cleanly without becoming non-recombining. Trinomials also integrate naturally with explicit finite difference schemes - a trinomial step with probabilities p_u, p_m, p_d matches a central-difference discretization of the PDE. For calibration, you apply Arrow-Debreu displacement to shift the tree to match the input term structure exactly. ```mermaid graph TD N[Rate
node] --> U[Up] N --> M[Middle] N --> D[Down] ``` Our FRM rate modeling lessons cover Hull-White calibration in detail.

Why do interest rate models use trinomial trees instead of binomial?

Master Part I with our FRM Course

Related Questions

Practice Questions