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Lognormality of Rates and Term Structure Models

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  • Goldys, B.
  • M. Musiela
  • D. Sondermann
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    Abstract

    A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain positive. They are bounded from below and above by lognormal processes. The model can be used to price and hedge caps, swaptions and other interest rate and currency derivatives including the Eurodollar futures contract, which requires integrability of one over zero coupon bond. This extends results obtained by Sandmann and Sondermann (1993), (1994) for Markovian lognormal short rates to (non-Markovian) lognormal forward rates.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb394.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 394.

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    Length: pages
    Date of creation: Nov 1996
    Date of revision:
    Handle: RePEc:bon:bonsfb:394

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    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: Term structure of interest rates; lognormal volatility structure; Heath; Jarrow and Morton models.;

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    References

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    1. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
    2. K. Sandmann & Sondermann, D., 1993. "A Term Structure Model and the Pricing of Interest Rate Derivative," Discussion Paper Serie B 180, University of Bonn, Germany.
    3. Farshid Jamshidian, 1993. "Option and Futures Evaluation With Deterministic Volatilities," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 149-159.
    4. D. Sondermann & Sandmann, K., 1994. "On the Stability of Log-Normal Interest Rate Models and the Pricing of Eurodollar Futures," Discussion Paper Serie B 263, University of Bonn, Germany.
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