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Models of forward Libor and swap rates

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  • Marek Rutkowski

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.

Suggested Citation

  • Marek Rutkowski, 1999. "Models of forward Libor and swap rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(1), pages 29-60.
    • Handle: RePEc:taf:apmtfi:v:6:y:1999:i:1:p:29-60
    DOI: 10.1080/135048699334609
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    References listed on IDEAS

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Marek Rutkowski, 1998. "Dynamics of Spot, Forward, and Futures Libor Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 425-445.
    3. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    5. Glasserman, P. & Zhao, X., 1998. "Arbitrage-Free Discretization of Lognormal Forward Libor and Swap Rate Models," Papers 98-09, Columbia - Graduate School of Business.
    6. 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.
    7. Ball, Clifford A. & Torous, Walter N., 1983. "Bond Price Dynamics and Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(4), pages 517-531, December.
    8. J.E. Kennedy & P.J. Hunt, 1998. "Implied interest rate pricing models," Finance and Stochastics, Springer, vol. 2(3), pages 275-293.
    9. Amin, Kaushik I & Ng, Victor K, 1997. "Inferring Future Volatility from the Information in Implied Volatility in Eurodollar Options: A New Approach," The Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 333-367.
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    Cited by:

    1. Sami Attaoui, 2011. "Hedging performance of the Libor market model: the cap market case," Post-Print hal-00653437, HAL.
    2. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    3. Marek Rutkowski & Matthew Bickersteth, 2021. "Pricing and Hedging of SOFR Derivatives under Differential Funding Costs and Collateralization," Papers 2112.14033, arXiv.org.
    4. Martino Grasselli & Giulio Miglietta, 2016. "A flexible spot multiple-curve model," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1465-1477, October.
    5. 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.

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