Additional Analytical Approximations of the Term Structure and Distributional Assumptions for Jump-Diffusion Processes

Abstract

Affine term structure models in which the short rate follows a jump-diffusion process are difficult to solve. Without analytical answers to the partial difference differential equation (PDDE) for bond prices implied by jump-diffusion processes, one must find a numerical solution to the PDDE or exactly solve an approximate PDDE. Although the literature focuses on a single linearization technique to estimate the PDDE, this article outlines alternative methods that seem to improve accuracy. Also, closed form solutions, numerical estimates, and closed form approximations of the PDDE each ultimately depend on the presumed distribution of jump sizes, and this article explores a broader set of possible densities more consistent with intuition.