Keywords: Jump-diffusion, term-structure models
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.
Full paper (265 KB PDF)
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Last update: December 3, 2005