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Calibration of Multicurrency LIBOR Market Models

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Abstract

This paper presents a methodf or calibrating a multi currency lognormal LIBOR Market Model to market data of at-the-money caps, swaptions and FX options. By exploiting the fact that multivariate normal distributions are invariant under orthonormal transformations, the calibration problem is decomposed into manageable stages, while maintaining the ability to achieve realistic correlation structures between all modelled market variables.

Suggested Citation

  • Kay Pilz & Erik Schlogl, 2010. "Calibration of Multicurrency LIBOR Market Models," Research Paper Series 286, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:286
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp286.pdf
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    References listed on IDEAS

    as
    1. Bruce Choy & Tim Dun & Erik Schlögl, 2003. "Correlating Market Models," Research Paper Series 105, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    3. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    4. Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. 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.
    6. Kay Pilz & Erik Schlogl, 2009. "A Hybrid Commodity and Interest Rate," Research Paper Series 261, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Keywords

    currency options; LIBOR market model; exchange rate risk; interest rate risk;
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