A model of discontinuous interest rate behavior,yield curves,and volatility |
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Authors: | Steven L Heston |
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Institution: | (1) 4447 Van Munching Hall, University of Maryland, College Park, MD 20742, USA |
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Abstract: | This paper develops an equilibrium model in which interest rates follow a discontinuous (generalized) gamma process. The gamma
process has finite variation, takes an infinite number of “small” jumps in every interval, and includes the Wiener process
as a limiting case. The gamma interest rate model produces yield curves that closely resemble those of diffusion models. But
in contrast to diffusion models, the curvature of the yield curve does not directly depend on the true volatility of the interest
rate process, but instead depends on a different risk-neutral volatility. The gamma model appears to fit the distribution
of interest rates changes and the jump characteristics of interest rate paths. Empirical tests reject a diffusion model of
interest rates in favor of the more general gamma model because daily interest rate innovations are highly leptokurtic.
The author appreciates comments from George Constantinides, Jon Ingersoll, Herbert Johnson, Ray Rishel, and an anonymous referee,
computational assistance from Kerry Back and Saikat Nandi, and support from Atlantic Asset Management. Any errors are the
responsibility of the author. |
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Keywords: | Interest rates Yield curve Levy process |
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