96-010
ANALYTICAL APPROXIMATIONS OF THE TERM STRUCTURE FOR JUMP-DIFFUSION PROCESSES: A NUMERICAL ANALYSIS
Jamil Baz and Sanjiv R. Das
Exact solutions to term structure models when interest rates follow jump-diffusions are hard to achieve. This paper obtains a solution to a jump-extended Vasicek (1977) model of interest rates by using an appropriate linearization of the fundamental partial differential-difference equation (PDDE) for the price of a zero-coupon bond. This solution is benchmarked against the numerical solution to the exact PDDE and is found to be extremely accurate over a range of plausible parameter values. While an exact solution to the extended Vasicek model is not possible for Gaussian jumps nor for constant jump sizes, the accuracy of the solution in this paper bodes well for the future ability to build jump-diffusion models for bond pricing when jumps may be allowed to follow a wide variety of distributions.
FIN
23 pages
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