IDEAS home Printed from
   My bibliography  Save this article

Robustness of the Black-Scholes approach in the case of options on several assets


  • Tiziano Vargiolu

    () (Dipartimento di Matematica Pura ed Applicata, Universitá di Padova, Via Belzoni 7, 35131 Padova, Italy Manuscript)

  • Silvia Romagnoli

    () (Istituto di Matematica Generale e Finanziaria, Universitá di Bologna, Piazza Scaravilli 2, 40139 Bologna, Italy)


In this paper we analyse a stochastic volatility model that is an extension of the traditional Black-Scholes one. We price European options on several assets by using a superstrategy approach. We characterize the Markov superstrategies, and show that they are linked to a nonlinear PDE, called the Black-Scholes-Barenblatt (BSB) equation. This equation is the Hamilton-Jacobi-Bellman equation of an optimal control problem, which has a nice financial interpretation. Then we analyse the optimization problem included in the BSB equation and give some sufficient conditions for reduction of the BSB equation to a linear Black-Scholes equation. Some examples are given.

Suggested Citation

  • Tiziano Vargiolu & Silvia Romagnoli, 2000. "Robustness of the Black-Scholes approach in the case of options on several assets," Finance and Stochastics, Springer, vol. 4(3), pages 325-341.
  • Handle: RePEc:spr:finsto:v:4:y:2000:i:3:p:325-341
    Note: received: April 1998; final revision received: May 1999

    Download full text from publisher

    File URL:
    Download Restriction: Access to the full text of the articles in this series is restricted

    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. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999,
    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. Peter Bank & Yan Dolinsky & Ari-Pekka Perkkiö, 2017. "The scaling limit of superreplication prices with small transaction costs in the multivariate case," Finance and Stochastics, Springer, vol. 21(2), pages 487-508, April.
    4. Rasmussen, Nicki Søndergaard, 2002. "Hedging with a Misspecified Model," Finance Working Papers 02-15, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    5. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

    More about this item


    stochastic volatility; superreplication; stochastic optimal control; Hamilton-Jacobi-Bellman equations;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


    Access and download statistics


    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:spr:finsto:v:4:y:2000:i:3:p:325-341. 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: (Sonal Shukla) or (Rebekah McClure). 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.