A Heuristic Algorithm for the Heath–Jarrow–Morton Model

Abstract

Heath–Jarrow–Morton [1990, 1991, and 1992] presented a general, intuitively appealing, term structure model for pricing interest rate claims. However, in discrete time, the model results in a non-recombining tree for many general deterministic volatility structures, which can be relatively computationally expensive when the number of time steps is large. This article provides a technique that combines interpolation with sparse ad-hoc mesh generation for valuing interest rate claims in the Heath–Jarrow–Morton framework. When this approach is used, the number of nodes in the mesh is significantly reduced without sacrificing accuracy. This article shows that with proper choice of nodes, the method will converge.