IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.04946.html
   My bibliography  Save this paper

A pathwise approach to continuous-time trading

Author

Listed:
  • Candia Riga

Abstract

This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a pathwise self-financial condition for continuous-time trading strategies, which is consistent with the classical definition in case a probability model is introduced. Our first proposition provides us with a pathwise definition of the gain process for a large class of continuous-time, path-dependent, self-finacing trading strategies, including the important class of 'delta-hedging' strategies, and is based on the recently developed 'non-anticipative functional calculus'. Two versions of the statement involve respectively continuous and c\`adl\`ag price paths. The second proposition is a pathwise replication result that generalizes the ones obtained in the classical framework of diffusion models. Moreover, it gives an explicit and purely pathwise formula for the hedging error of delta-hedging strategies for path-dependent derivatives across a given set of scenarios. We also provide an economic justification of our main assumption on price paths.

Suggested Citation

  • Candia Riga, 2016. "A pathwise approach to continuous-time trading," Papers 1602.04946, arXiv.org.
    • Handle: RePEc:arx:papers:1602.04946
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.04946
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Łochowski, Rafał M. & Perkowski, Nicolas & Prömel, David J., 2018. "A superhedging approach to stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4078-4103.
    2. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Numerical method for model-free pricing of exotic derivatives using rough path signatures," Papers 1905.01720, arXiv.org, revised Feb 2020.
    3. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2016. "A superhedging approach to stochastic integration," Papers 1609.02349, arXiv.org, revised Sep 2017.
    4. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Nonparametric pricing and hedging of exotic derivatives," Papers 1905.00711, arXiv.org.
    5. Jasdeep Kalsi & Terry Lyons & Imanol Perez Arribas, 2019. "Optimal execution with rough path signatures," Papers 1905.00728, arXiv.org.
    6. Owen Futter & Blanka Horvath & Magnus Wiese, 2023. "Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals," Papers 2308.15135, arXiv.org, revised Aug 2023.
    7. Jani Lukkarinen & Mikko S. Pakkanen, 2016. "Arbitrage without borrowing or short selling?," Papers 1604.07690, arXiv.org, revised Oct 2016.
    8. Mikko S. Pakkanen & Jani Lukkarinen, 2016. "Arbitrage without borrowing or short selling?," CREATES Research Papers 2016-13, Department of Economics and Business Economics, Aarhus University.
    9. Andrew L. Allan & Chong Liu & David J. Promel, 2021. "A C\`adl\`ag Rough Path Foundation for Robust Finance," Papers 2109.04225, arXiv.org, revised May 2023.

    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. Frank Riedel, 2011. "Finance Without Probabilistic Prior Assumptions," Papers 1107.1078, arXiv.org.
    2. Schied, Alexander, 2014. "Model-free CPPI," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 84-94.
    3. Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
    4. Hans Follmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    5. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    6. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
    7. 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.
    8. Henry Chiu & Rama Cont, 2023. "A model‐free approach to continuous‐time finance," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 257-273, April.
    9. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
    10. Alexander Schied, 2013. "Model-free CPPI," Papers 1305.5915, arXiv.org, revised Jan 2014.
    11. 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.
    12. David Hobson & Martin Klimmek, 2012. "Model-independent hedging strategies for variance swaps," Finance and Stochastics, Springer, vol. 16(4), pages 611-649, October.
    13. Alexander Schied, 2015. "On a class of generalized Takagi functions with linear pathwise quadratic variation," Papers 1501.00837, arXiv.org, revised Aug 2015.
    14. Rimas Norvaiša & Donna Mary Salopek, 2002. "Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 27-53, March.
    15. Henry Chiu & Rama Cont, 2022. "A model-free approach to continuous-time finance," Papers 2211.15531, arXiv.org.
    16. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2016. "A superhedging approach to stochastic integration," Papers 1609.02349, arXiv.org, revised Sep 2017.
    17. David Hobson & Martin Klimmek, 2011. "Model independent hedging strategies for variance swaps," Papers 1104.4010, arXiv.org, revised May 2011.
    18. 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.
    19. Alexander Alvarez & Sebastian Ferrando & Pablo Olivares, 2011. "Arbitrage and Hedging in a non probabilistic framework," Papers 1103.1006, arXiv.org.
    20. Łochowski, Rafał M. & Perkowski, Nicolas & Prömel, David J., 2018. "A superhedging approach to stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4078-4103.

    More about this item

    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:1602.04946. 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.