IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1103.1006.html
   My bibliography  Save this paper

Arbitrage and Hedging in a non probabilistic framework

Author

Listed:
  • Alexander Alvarez

    (Ryerson University, Toronto)

  • Sebastian Ferrando

    (Ryerson University, Toronto)

  • Pablo Olivares

    (Ryerson University, Toronto)

Abstract

The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual notion of arbitrage. Several examples illustrate the non probabilistic arbitrage as well perfect replication of options under continuous and discontinuous trajectories, the results can then be applied in probabilistic models path by path. The approach is related to recent financial models that go beyond semimartingales, we remark on some of these connections and provide applications of our results to some of these models.

Suggested Citation

  • Alexander Alvarez & Sebastian Ferrando & Pablo Olivares, 2011. "Arbitrage and Hedging in a non probabilistic framework," Papers 1103.1006, arXiv.org.
    • Handle: RePEc:arx:papers:1103.1006
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1103.1006
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
    2. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    3. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schied, Alexander, 2014. "Model-free CPPI," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 84-94.
    2. Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
    3. John Armstrong & Claudio Bellani & Damiano Brigo & Thomas Cass, 2021. "Option pricing models without probability: a rough paths approach," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1494-1521, October.
    4. Alexander Schied, 2013. "Model-free CPPI," Papers 1305.5915, arXiv.org, revised Jan 2014.
    5. Alexander Alvarez & Sebastian E. Ferrando, 2016. "Trajectory-Based Models, Arbitrage And Continuity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-34, May.
    6. Alexander Schied, 2015. "On a class of generalized Takagi functions with linear pathwise quadratic variation," Papers 1501.00837, arXiv.org, revised Aug 2015.
    7. Frank Riedel, 2015. "Financial economics without probabilistic prior assumptions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 75-91, April.
    8. Alexander Schied & Iryna Voloshchenko, 2015. "Pathwise no-arbitrage in a class of Delta hedging strategies," Papers 1511.00026, arXiv.org, revised Jun 2016.
    9. Flandreau, Marc & Komlos, John, 2006. "Target zones in theory and history: Credibility, efficiency, and policy autonomy," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1979-1995, November.
    10. Tejada, César A. O. & Portugal, Marcelo S., 2002. "Credibility and Reputation: An Application of the External Circumstances Model for the Real Plan," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 56(4), October.
    11. Eyal Neuman & Alexander Schied, 2018. "Protecting Pegged Currency Markets from Speculative Investors," Papers 1801.07784, arXiv.org, revised Feb 2021.
    12. Sutherland, Alan, 1995. "Monetary and real shocks and the optimal target zone," European Economic Review, Elsevier, vol. 39(1), pages 161-172, January.
    13. Ken Miyajima, 2013. "Foreign exchange intervention and expectation in emerging economies," BIS Working Papers 414, Bank for International Settlements.
    14. Seungwook Bahng, 2003. "Do Psychological Barriers Exist in the Stock Price Indices? Evidence from Asia's Emerging Markets," International Area Studies Review, Center for International Area Studies, Hankuk University of Foreign Studies, vol. 6(1), pages 35-52, March.
    15. Maurice Obstfeld & Jay C. Shambaugh & Alan M. Taylor, 2005. "The Trilemma in History: Tradeoffs Among Exchange Rates, Monetary Policies, and Capital Mobility," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 423-438, August.
    16. Ulf Söderström & Alexis Stenfors, 1995. "Explaining devaluation expectations in the EMS," Finnish Economic Papers, Finnish Economic Association, vol. 8(2), pages 63-81, Autumn.
    17. Jukka Isohätälä & Alistair Milne & Donald Robertson, 2020. "The Net Worth Trap: Investment and Output Dynamics in the Presence of Financing Constraints," Mathematics, MDPI, vol. 8(8), pages 1-32, August.
    18. Chen Yu-Fu & Funke Michael & Glanemann Nicole, 2013. "Off-the-record target zones: theory with an application to Hong Kong’s currency board," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(4), pages 373-393, September.
    19. Bai, Yizhou & Xue, Cheng, 2021. "An empirical study on the regulated Chinese agricultural commodity futures market based on skew Ornstein-Uhlenbeck model," Research in International Business and Finance, Elsevier, vol. 57(C).
    20. Erhan Bayraktar & Mikko S. Pakkanen & Hasanjan Sayit, 2009. "On the Existence of Consistent Price Systems," Papers 0911.3789, arXiv.org, revised Jun 2013.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:arx:papers:1103.1006. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.