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Long-Term Returns in Stochastic Interest Rate Models: Applications

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  • Deelstra, Griselda

Abstract

We extend the Cox-Ingersoll-Ross (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the long-term return by using the theory of generalised Bessel-square processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral . For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very time-consuming.

Suggested Citation

  • Deelstra, Griselda, 2000. "Long-Term Returns in Stochastic Interest Rate Models: Applications," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 123-140, May.
    • Handle: RePEc:cup:astinb:v:30:y:2000:i:01:p:123-140_00
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    Cited by:

    1. Zhao, Juan, 2009. "Long time behaviour of stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 459-463, June.
    2. Agić-Šabeta Elma, 2016. "Constant Proportion Portfolio Insurance Strategy in Southeast European Markets," Business Systems Research, Sciendo, vol. 7(1), pages 59-80, March.
    3. Duc, Luu Hoang & Tran, Tat Dat & Jost, Jürgen, 2018. "Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3253-3272.
    4. Jan de Kort, 2018. "A note on the long rate in factor models of the term structure," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 656-667, April.

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