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

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  • Wolfgang Kluge
  • Antonis Papapantoleon

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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  • Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in L\'evy term structure models," Papers 0902.3456, arXiv.org.
    • Handle: RePEc:arx:papers:0902.3456
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    File URL: http://arxiv.org/pdf/0902.3456
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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. Maria Siopacha & Josef Teichmann, 2007. "Weak and Strong Taylor methods for numerical solutions of stochastic differential equations," Papers 0704.0745, arXiv.org.
    3. 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..
    4. 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.
    5. Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance 0407018, University Library of Munich, Germany, revised 27 Sep 2005.
    6. Robert Jarrow, 2017. "Derivatives," World Scientific Book Chapters, in: THE ECONOMIC FOUNDATIONS OF RISK MANAGEMENT Theory, Practice, and Applications, chapter 3, pages 19-28, World Scientific Publishing Co. Pte. Ltd..
    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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    Cited by:

    1. Kathrin Glau & Zorana Grbac & Antonis Papapantoleon, 2016. "A unified view of LIBOR models," Papers 1601.01352, arXiv.org, revised Jul 2016.
    2. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 257-275.
    3. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(3), pages 257-275, August.

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