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The Processes of Short-Term Interest Rates and Their Probability Densities

In: Yield Curves and Forward Curves for Diffusion Models of Short Rates

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  • Gennady A. Medvedev

    (Belarusian State University)

Abstract

In this chapter we deal with marginal probability densities of diffusion type processes, generated by sixteen models of short-term interest rates, which allow us to obtain densities in analytical form. This family covers almost all currently used models of continuous time. Some densities (Vasiček, Cox–Ingersoll–Ross, geometric Brownian motionGeometric Brownian motion , Ahn–Gao) are well studied in the literature and are given here for convenience of comparison. Other densities are described for the first time. The main focus is on the analytical properties of densities and their four first moments (mathematical expectation, variance, asymmetry and kurtosis)Kurtosis , which are most often of interest to practitioners. In the main, stationary densities and moments are considered, although several models generate non-stationary processes.

Suggested Citation

  • Gennady A. Medvedev, 2019. "The Processes of Short-Term Interest Rates and Their Probability Densities," Springer Books, in: Yield Curves and Forward Curves for Diffusion Models of Short Rates, chapter 0, pages 1-18, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15500-1_1
    DOI: 10.1007/978-3-030-15500-1_1
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