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Financial Models with Defaultable Numéraires

Author

Listed:
  • Travis Fisher
  • Sergio Pulido

    (ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise, LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique)

  • Johannes Ruf

    (Department of Mathematics London School of Economics - LSE - London School of Economics and Political Science)

Abstract

Financial models are studied where each asset may potentially lose value relative to any other. Conditioning on non-devaluation, each asset can serve as proper numéraire and classical valuation rules can be formulated. It is shown when and how these local valuation rules can be aggregated to obtain global arbitrage-free valuation formulas.

Suggested Citation

  • Travis Fisher & Sergio Pulido & Johannes Ruf, 2019. "Financial Models with Defaultable Numéraires," Post-Print hal-01240736, HAL.
    • Handle: RePEc:hal:journl:hal-01240736
    DOI: 10.1111/mafi.12178
    Note: View the original document on HAL open archive server: https://hal.science/hal-01240736v4
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    References listed on IDEAS

    as
    1. Steven L. Heston & Mark Loewenstein & Gregory A. Willard, 2007. "Options and Bubbles," The Review of Financial Studies, Society for Financial Studies, vol. 20(2), pages 359-390.
    2. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    3. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, August.
    4. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    5. António Câmara & Steven L. Heston, 2008. "Closed‐form option pricing formulas with extreme events," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(3), pages 213-230, March.
    6. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
    7. Kardaras, Constantinos, 2015. "Valuation and parities for exchange options," LSE Research Online Documents on Economics 65535, London School of Economics and Political Science, LSE Library.
    8. Louis Paulot, 2013. "Arbitrage-Free Pricing Before and Beyond Probabilities," Papers 1310.1102, arXiv.org.
    9. Peter Carr & Travis Fisher & Johannes Ruf, 2012. "Why are quadratic normal volatility models analytically tractable?," Papers 1202.6187, arXiv.org, revised Mar 2013.
    10. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    11. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    12. Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Černý, Aleš & Ruf, Johannes, 2020. "Simplified stochastic calculus with applications in economics and finance," LSE Research Online Documents on Economics 108156, London School of Economics and Political Science, LSE Library.
    2. Černý, Aleš & Ruf, Johannes, 2021. "Simplified stochastic calculus with applications in Economics and Finance," European Journal of Operational Research, Elsevier, vol. 293(2), pages 547-560.

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    More about this item

    Keywords

    Devaluation; Non-classical valuation formulas; Defaultable numéraire;
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