IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1004.3577.html
   My bibliography  Save this paper

Fractional smoothness and applications in finance

Author

Listed:
  • Stefan Geiss
  • Emmanuel Gobet

Abstract

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.

Suggested Citation

  • Stefan Geiss & Emmanuel Gobet, 2010. "Fractional smoothness and applications in finance," Papers 1004.3577, arXiv.org.
  • Handle: RePEc:arx:papers:1004.3577
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1004.3577
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Geiss, Christel & Geiss, Stefan, 2006. "On an approximation problem for stochastic integrals where random time nets do not help," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 407-422, March.
    2. Takaki Hayashi & Per A. Mykland, 2005. "Evaluating Hedging Errors: An Asymptotic Approach," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 309-343, April.
    3. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    4. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    5. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    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. Stefan Geiss & Emmanuel Gobet, 2011. "Fractional smoothness and applications in Finance," Post-Print hal-00474803, HAL.
    2. Mats Brod'en & Magnus Wiktorsson, 2010. "Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy," Papers 1004.4526, arXiv.org.
    3. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833, arXiv.org, revised Jul 2017.
    4. Wang, Wensheng, 2019. "Asymptotics for discrete time hedging errors under fractional Black–Scholes models," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 160-170.
    5. Gobet, Emmanuel & Makhlouf, Azmi, 2010. "-time regularity of BSDEs with irregular terminal functions," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1105-1132, July.
    6. Mats Brod'en & Peter Tankov, 2010. "Tracking errors from discrete hedging in exponential L\'evy models," Papers 1003.0709, arXiv.org.
    7. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    8. Masaaki Fukasawa, 2012. "Efficient Discretization of Stochastic Integrals," Papers 1204.0637, arXiv.org.
    9. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    10. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    11. Masaaki Fujii & Akihiko Takahashi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 283-304, September.
    12. Gobet, Emmanuel & Labart, Céline, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.
    13. Giorgia Callegaro & Alessandro Gnoatto & Martino Grasselli, 2021. "A Fully Quantization-based Scheme for FBSDEs," Working Papers 07/2021, University of Verona, Department of Economics.
    14. Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
    15. Lucio Fiorin & Gilles Pagès & Abass Sagna, 2019. "Product Markovian Quantization of a Diffusion Process with Applications to Finance," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1087-1118, December.
    16. Masaaki Fujii & Akihiko Takahashi, 2016. "Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions," Papers 1606.04285, arXiv.org, revised May 2018.
    17. Asaf Cohen & Yan Dolinsky, 2022. "A scaling limit for utility indifference prices in the discretised Bachelier model," Finance and Stochastics, Springer, vol. 26(2), pages 335-358, April.
    18. dos Reis, Gonçalo & Réveillac, Anthony & Zhang, Jianing, 2011. "FBSDEs with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2114-2150, September.
    19. Andrew Lesniewski & Anja Richter, 2016. "Managing counterparty credit risk via BSDEs," Papers 1608.03237, arXiv.org, revised Aug 2016.
    20. Pelsser Antoon & Gnameho Kossi, 2019. "A Monte Carlo method for backward stochastic differential equations with Hermite martingales," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 37-60, March.

    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:1004.3577. 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.