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A cross-currency Levy market model

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  • Ernst Eberlein
  • Nataliya Koval
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    Abstract

    The Levy Libor or market model which was introduced in Eberlein and Ozkan (The Levy Libor model. Financ. Stochast., 2005, 9, 327-348) is extended to a multi-currency setting. As an application we derive closed form pricing formulas for cross-currency derivatives. Foreign caps and floors and cross-currency swaps are studied in detail. Numerically efficient pricing algorithms based on bilateral Laplace transforms are derived. A calibration example is given for a two-currency setting (EUR, USD).

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680600818791
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    Bibliographic Info

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

    Volume (Year): 6 (2006)
    Issue (Month): 6 ()
    Pages: 465-480

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    Handle: RePEc:taf:quantf:v:6:y:2006:i:6:p:465-480

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    Related research

    Keywords: Multi-currency model; Cross-currency derivatives; Foreign forward caps and floors; Cross-currency swaps; Time-inhomogeneous Levy processes; Forward martingale measure;

    References

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    1. 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.
    2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    3. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53.
    4. 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.
    5. Erik Schlögl, 1999. "A Multicurrency Extension of the Lognormal Interest Rate Market Models," Research Paper Series 20, Quantitative Finance Research Centre, University of Technology, Sydney.
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