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Pricing vulnerable claims in a Lévy-driven model

Author

Listed:
  • Agostino Capponi
  • Stefano Pagliarani
  • Tiziano Vargiolu

Abstract

We obtain an explicit expression for the price of a vulnerable claim written on a stock whose predefault dynamics follows a Lévy-driven SDE. The stock jumps to zero at default with a hazard rate given by a negative power of the stock price. We recover the characteristic function of the terminal log price as the solution of an infinite-dimensional system of complex-valued first-order ordinary differential equations. We provide an explicit eigenfunction expansion representation of the characteristic function in a suitably chosen Banach space and use it to price defaultable bonds and stock options. We present numerical results to demonstrate the accuracy and efficiency of the method. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Agostino Capponi & Stefano Pagliarani & Tiziano Vargiolu, 2014. "Pricing vulnerable claims in a Lévy-driven model," Finance and Stochastics, Springer, vol. 18(4), pages 755-789, October.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:4:p:755-789
    DOI: 10.1007/s00780-014-0239-6
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    References listed on IDEAS

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    9. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
    10. Akihiko Takahashi & Takao Kobayashi & Naruhisa Nakagawa, 2001. "Pricing Convertible Bonds with Default Risk: A Duffie-Singleton Approach," CIRJE F-Series CIRJE-F-140, CIRJE, Faculty of Economics, University of Tokyo.
    11. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A family of density expansions for L\'evy-type processes," Papers 1312.7328, arXiv.org.
    12. Peter Carr & Liuren Wu, 2011. "A Simple Robust Link Between American Puts and Credit Protection," The Review of Financial Studies, Society for Financial Studies, vol. 24(2), pages 473-505.
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    Citations

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    Cited by:

    1. Anastasia Borovykh & Andrea Pascucci & Cornelis W. Oosterlee, 2019. "Efficient Computation of Various Valuation Adjustments Under Local L\'evy Models," Papers 1905.01706, arXiv.org.
    2. F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "CVA and vulnerable options pricing by correlation expansions," Annals of Operations Research, Springer, vol. 299(1), pages 401-427, April.
    3. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    4. Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2022. "Approximate value adjustments for European claims," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1149-1161.
    5. Anastasia Borovykh & Cornelis W. Oosterlee & Andrea Pascucci, 2016. "Pricing Bermudan options under local L\'evy models with default," Papers 1604.08735, arXiv.org.
    6. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A family of density expansions for L\'evy-type processes," Papers 1312.7328, arXiv.org.

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    More about this item

    Keywords

    Default; Infinite-dimensional analysis; Vulnerable claims; Lévy process; Characteristic function; 60J60; 60J65; 60G70; 60G75; G12; G13;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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