Jump-Diffusion Processes and Affine Term Structure Models: Additional Closed-Form Approximate Solutions, Distributional Assumptions for Jumps, and Parameter Estimates

59 Pages Posted: 5 Jan 2006

Date Written: November 2005

Abstract

Affine term structure models in which the short rate follows a jump-diffusion process are difficult to solve, and the parameters of such models are hard to estimate. 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 paper 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 paper explores a broader set of possible densities that may be more consistent with intuition, including a bi-modal Gaussian mixture. GMM and MLE of one- and two-factor jump-diffusion models produce some evidence for jumps, but sensitivity analyses suggest sizeable confidence intervals around the parameters.

Keywords: Jump-diffusion, term-structure models

JEL Classification: E43

Suggested Citation

Durham, J. Benson, Jump-Diffusion Processes and Affine Term Structure Models: Additional Closed-Form Approximate Solutions, Distributional Assumptions for Jumps, and Parameter Estimates (November 2005). FEDs Working Paper No. 2005-53. Available at SSRN: https://ssrn.com/abstract=873870 or http://dx.doi.org/10.2139/ssrn.873870

J. Benson Durham (Contact Author)

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