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Models of forward Libor and swap rates

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  • Marek Rutkowski
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    Abstract

    The backward induction approach is systematically used to produce various models of forward market rates. These include the lognormal model of forward Libor rates examined by Miltersen et al. and Brace et al., as well as the lognormal model of (fixed-maturity) forward swap rates, which was proposed by Jamshidian. The valuation formulae for European caps and swaptions are given. In the last section, the Eurodollar futures contracts and options are examined within the framework of the lognormal model of forward Libor rates.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 6 (1999)
    Issue (Month): 1 ()
    Pages: 29-60

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    Handle: RePEc:taf:apmtfi:v:6:y:1999:i:1:p:29-60

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    Related research

    Keywords: Zero-coupon Bond; Libor Rate; Swap Rate; Swaption; Eurodollar Futures;

    References

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    1. Ball, Clifford A. & Torous, Walter N., 1983. "Bond Price Dynamics and Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(04), pages 517-531, December.
    2. Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
    3. Amin, Kaushik I & Ng, Victor K, 1997. "Inferring Future Volatility from the Information in Implied Volatility in Eurodollar Options: A New Approach," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 333-67.
    4. Glasserman, P. & Zhao, X., 1998. "Arbitrage-Free Discretization of Lognormal Forward Libor and Swap Rate Models," Papers 98-09, Columbia - Graduate School of Business.
    5. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    6. J.E. Kennedy & P.J. Hunt, 1998. "Implied interest rate pricing models," Finance and Stochastics, Springer, vol. 2(3), pages 275-293.
    7. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    8. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
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