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The Sustainable Black-Scholes Equations

Author

Listed:
  • Yannick Armenti

    (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)

  • Stéphane Crépey

    (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)

  • Chao Zhou

    (Department of Mathematics [Singapore] - NUS - National University of Singapore)

Abstract

In incomplete markets, a basic Black-Scholes perspective has to be complemented by the valuation of market imperfections. Otherwise this results in Black-Scholes Ponzi schemes, such as the ones at the core of the last global financial crisis, where always more derivatives need to be issued for remunerating the capital attracted by the already opened positions. In this paper we consider the sustainable Black-Scholes equations that arise for a portfolio of options if one adds to their trade additive Black-Scholes price, on top of a nonlinear funding cost, the cost of remunerating at a hurdle rate the residual risk left by imperfect hedging. We assess the impact of model uncertainty in this setup.

Suggested Citation

  • Yannick Armenti & Stéphane Crépey & Chao Zhou, 2018. "The Sustainable Black-Scholes Equations," Working Papers hal-01764397, HAL.
    • Handle: RePEc:hal:wpaper:hal-01764397
    Note: View the original document on HAL open archive server: https://hal.science/hal-01764397
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    References listed on IDEAS

    as
    1. Claudio Albanese & Simone Caenazzo & Stéphane Crépey, 2016. "Capital Valuation Adjustment and Funding Valuation Adjustment," Working Papers hal-01285363, HAL.
    2. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
    3. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
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    More about this item

    Keywords

    Market incompleteness; cost of capital (KVA); cost of funding (FVA); model risk; volatility uncertainty; optimal martingale transport;
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