A model of discontinuous interest rate behavior,yield curves,and volatility

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.