A Unified Willow Tree Framework for One-Factor Short-Rate Models

Abstract

The familiar binomial model allows the stock to move from the current node to just two possible prices in the next time step, which seriously limits the model’s ability to handle many realistic problems efficiently. The trinomial adds a branch and gains a lot more flexibility. The “willow tree” structure allows many branches at each node, and recent work has shown that it can produce significant improvements in performance for some classes of problems. Modeling interest rate behavior is an extremely important case. A viable short-rate model must allow stochastic volatility, and for practical use it must be arbitrage-free, meaning it can be calibrated to match the observed term structure of forward rates in the market. In this article, Wang and Xu show how to construct willow tree lattice models for eleven of the most common single-factor interest rate models, including those designed to be arbitrage-free. Unlike some of these models, the willow tree approach can handle interest rates that go negative, which is essential in the current environment.