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On the valuation of compositions in L\'evy term structure models

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  • Wolfgang Kluge
  • Antonis Papapantoleon
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    Abstract

    We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models for the evolution of interest rates: an HJM-type forward rate model and a LIBOR-type forward price model. Both models are driven by a time-inhomogeneous L\'evy process.

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    File URL: http://arxiv.org/pdf/0902.3456
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0902.3456.

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    Date of creation: Feb 2009
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    Publication status: Published in Quantitative Finance 2009, Vol. 9, No. 8, 951-959
    Handle: RePEc:arx:papers:0902.3456

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    Web page: http://arxiv.org/

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, Springer, vol. 1(4), pages 293-330.
    2. 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, American Finance Association, vol. 52(1), pages 409-30, March.
    3. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 167-179.
    4. Maria Siopacha & Josef Teichmann, 2007. "Weak and Strong Taylor methods for numerical solutions of stochastic differential equations," Papers 0704.0745, arXiv.org.
    5. Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance, EconWPA 0407018, EconWPA, revised 14 Aug 2004.
    6. 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, Econometric Society, vol. 60(1), pages 77-105, January.
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