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A note on pricing interest rate derivatives when forward LIBOR rates are lognormal

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  • Beniamin Goldys

    (School of Mathematics, The University of New South Wales, Sydney 2052, Australia)

Abstract

We derive the closed form pricing formulae for contracts written on zero coupon bonds for the lognormal forward LIBOR rates. The method is purely probabilistic in contrast with the earlier results obtained by Miltersen et al. (1997).

Suggested Citation

  • Beniamin Goldys, 1997. "A note on pricing interest rate derivatives when forward LIBOR rates are lognormal," Finance and Stochastics, Springer, vol. 1(4), pages 345-352.
    • Handle: RePEc:spr:finsto:v:1:y:1997:i:4:p:345-352
    Note: received: November 1995; final version received: June 1997
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    References listed on IDEAS

    as
    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 409-430, March.
    2. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    3. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    4. Rady, Sven, 1994. "The Direct Approach to Debt Option Pricing," Munich Reprints in Economics 3404, University of Munich, Department of Economics.
    5. Klaus Sandmann & Dieter Sondermann, 1997. "A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 119-125, April.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Peter Carr & Travis Fisher & Johannes Ruf, 2012. "Why are quadratic normal volatility models analytically tractable?," Papers 1202.6187, arXiv.org, revised Mar 2013.
    2. Zühlsdorff, Christian, 2002. "The Pricing of Derivatives on Assets with Quadratic Volatility," Bonn Econ Discussion Papers 5/2002, University of Bonn, Bonn Graduate School of Economics (BGSE).
    3. S. Galluccio & J.‐M. Ly & Z. Huang & O. Scaillet, 2007. "Theory And Calibration Of Swap Market Models," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 111-141, January.
    4. Bachmair, K., 2023. "The Effects of the LIBOR Scandal on Volatility and Liquidity in LIBOR Futures Markets," Cambridge Working Papers in Economics 2303, Faculty of Economics, University of Cambridge.
    5. Christian Zuhlsdorff, 2001. "The pricing of derivatives on assets with quadratic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 235-262.

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    More about this item

    Keywords

    Lognormal model of LIBOR rates; contracts on zero-coupon bonds; Girsanov transformation;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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