IDEAS home Printed from
   My bibliography  Save this article

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


  • Marco Avellaneda
  • Antonio ParAS


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.

Suggested Citation

  • Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 21-52.
  • Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:21-52 DOI: 10.1080/13504869600000002

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. 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.
    2. Breuer, Thomas & Csiszár, Imre, 2013. "Systematic stress tests with entropic plausibility constraints," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1552-1559.
    3. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    4. Jocelyne Bion-Nadal, 2007. "Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk," Papers math/0703074,
    5. Umberto Cherubini, 1997. "Fuzzy measures and asset prices: accounting for information ambiguity," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(3), pages 135-149.
    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. repec:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500050 is not listed on IDEAS
    8. Umberto Cherubini & Giovanni Della Lunga, 2001. "Liquidity and credit risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 79-95.
    9. repec:spr:finsto:v:21:y:2017:i:4:d:10.1007_s00780-017-0342-6 is not listed on IDEAS
    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. Thomas Breuer & Imre Csiszar, 2013. "Measuring Model Risk," Papers 1301.4832,
    12. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    13. Claude Bardos & Raphaël Douady & Andrei Fursikov, 2002. "Static Hedging Of Barrier Options With A Smile: An Inverse Problem," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01477102, HAL.
    14. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging," Papers 1704.04524,
    15. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    16. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2017. "Hedging with small uncertainty aversion," Finance and Stochastics, Springer, vol. 21(1), pages 1-64, January.
    17. Colino, Jesús P. & Nogales, Francisco J. & Stute, Winfried, 2008. "LIBOR additive model calibration to swaptions markets," DES - Working Papers. Statistics and Econometrics. WS ws085619, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. Kaj Nystrom & Mikko Parviainen, 2014. "Tug-of-war, market manipulation and option pricing," Papers 1410.1664,
    19. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2016. "Hedging with Small Uncertainty Aversion," Papers 1605.06429,
    20. 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.
    21. Nicole Branger & Antje Mahayni, 2011. "Tractable hedging with additional hedge instruments," Review of Derivatives Research, Springer, vol. 14(1), pages 85-114, April.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:21-52. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.