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The Duffie–Kan Two-Factor Models

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

Author

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  • Gennady A. Medvedev

    (Belarusian State University)

Abstract

In this chapterTwo-factor model we analyze the Duffie–Kan modelsDuffie–Kan model that describe the dynamics of a short-term interest rate in the case when the state of the financial marketState of financial market is characterized not only by the level of the interest rate itself, but also by another other time-varying parameter. Two cases are considered. In the first, the local-time average of the short-term interest rate is taken as an additional state variableState variable . In the second case, the instantaneous variance of the interest rate is adopted as an additional state variable. Two-factor models are constructed in such a way that they lead to an affine time structure of interest rate. The main focus is on the definition of the functions of the term structure. Since the equations obtained for these functions do not admit analytic solutions, it is proposed to find their approximations. In view of the fact that in real cases the volatility is usually small, Poincaré’s method of small parametersMethod of small parameter is used for this. Further, the same two cases are considered using a numerical approach. The focus is on the properties of the yield curveYield curve and the forward curveForward curve , when the dynamics of the short-term interest rate is described by the Duffie–Kan two-factor modelsTwo-factor model .

Suggested Citation

  • Gennady A. Medvedev, 2019. "The Duffie–Kan Two-Factor Models," Springer Books, in: Yield Curves and Forward Curves for Diffusion Models of Short Rates, chapter 0, pages 93-114, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15500-1_6
    DOI: 10.1007/978-3-030-15500-1_6
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