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Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model

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  • Marco Avellaneda
  • Antonio ParAS
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    Abstract

    We present an algorithm for hedging option portfolios and custom-tailored derivative securities, which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a non- linear partial differential equation to evaluate worst-case volatility scenarios for any given forward liability structure. This equation gives sub-additive portfolio prices and hence provides a natural ordering of prefer- ences in terms of hedging with options. The second element of the algorithm consists of a portfolio optim- ization taking into account the prices of options available in the market. Several examples are discussed, including possible applications to market-making in equity and foreign-exchange derivatives.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 3 (1996)
    Issue (Month): 1 ()
    Pages: 21-52

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    Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:21-52

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: Uncertain volatility; dynamic hedging; hedging with options;

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    Cited by:
    1. Nicole Branger & Antje Mahayni, 2011. "Tractable hedging with additional hedge instruments," Review of Derivatives Research, Springer, vol. 14(1), pages 85-114, April.
    2. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    3. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    4. Jesús P. Colino & Francisco J. Nogales & Winfried Stute, 2008. "LIBOR additive model calibration to swaptions markets," Statistics and Econometrics Working Papers ws085619, Universidad Carlos III, Departamento de Estadística y Econometría.
    5. Roy Kouwenberg & Jacek Gondzio & Ton Vorst, 1999. "Hedging Options under Transaction Costs and Stochastic Volatility," Computing in Economics and Finance 1999 911, Society for Computational Economics.
    6. Marco Avellaneda & Robert Buff, 1999. "Combinatorial implications of nonlinear uncertain volatility models: the case of barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(1), pages 1-18.
    7. Umberto Cherubini, 1997. "Fuzzy measures and asset prices: accounting for information ambiguity," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(3), pages 135-149.
    8. Umberto Cherubini & Giovanni Della Lunga, 2001. "Liquidity and credit risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 79-95.
    9. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    10. Ali Bora Yigibasioglu & Carol Alexandra, 2004. "An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds," ICMA Centre Discussion Papers in Finance icma-dp2004-07, Henley Business School, Reading University.
    11. Jocelyne Bion-Nadal, 2007. "Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk," Papers math/0703074, arXiv.org.
    12. Thomas Breuer & Imre Csiszar, 2013. "Measuring Model Risk," Papers 1301.4832, arXiv.org.
    13. Breuer, Thomas & Csiszár, Imre, 2013. "Systematic stress tests with entropic plausibility constraints," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1552-1559.
    14. Muzzioli, Silvia & Torricelli, Costanza, 2004. "A multiperiod binomial model for pricing options in a vague world," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 861-887, February.

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