Another Look at the Ho–Lee Bond Option Pricing Model

Abstract

Bond option pricing models come in two forms: equilibrium models and arbitrage-free models. The former start from assumptions about the dynamic process that governs the evolution of the instantaneous short rate, which produces a theoretically consistent model of the whole term structure. But unfortunately, real-world bond prices do not follow the model perfectly, and many will appear to be mispriced. By contrast, the Ho–Lee model, the first arbitrage-free model, starts with the observed term structure and sets up a binomial structure that determines how it can evolve over time so that there are no riskless arbitrage profit opportunities embedded in the current or any possible future yield curves. But the original formulation of the Ho–Lee model has the unfortunate property that it is possible for interest rates to go negative or to grow without bound over time, neither of which is acceptable. In this article, the authors present a modified Ho–Lee specification that eliminates the problem by allowing the binomial probabilities to change over time while still maintaining the no-arbitrage restriction.