IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1206.5983.html
   My bibliography  Save this paper

On a Symmetrization of Diffusion Processes

Author

Listed:
  • Jiro Akahori
  • Yuri Imamura

Abstract

The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the use of the numerical scheme for Heston or SABR type stochastic volatility models. This will be done by showing a fairly general result on the symmetrization (in multi-dimension/multi-reflections). Further applications (to time-inhomogeneous diffusions/ to time dependent boundaries/to curved boundaries) are also discussed.

Suggested Citation

  • Jiro Akahori & Yuri Imamura, 2012. "On a Symmetrization of Diffusion Processes," Papers 1206.5983, arXiv.org.
    • Handle: RePEc:arx:papers:1206.5983
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1206.5983
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Yuri Imamura & Katsuya Takagi, 2011. "Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion," Papers 1104.4548, arXiv.org, revised Oct 2012.
    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. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2018. "Asymptotic Static Hedge via Symmetrization," Papers 1801.04045, arXiv.org.
    2. Ngo, Hoang-Long & Taguchi, Dai, 2017. "Strong convergence for the Euler–Maruyama approximation of stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 55-63.
    3. Jiro Akahori & Flavia Barsotti & Yuri Imamura, 2017. "The Value of Timing Risk," Papers 1701.05695, arXiv.org.
    4. Yuri Imamura & Yuta Ishigaki & Takuya Kawagoe & Toshiki Okumura, 2012. "A Numerical Scheme Based on Semi-Static Hedging Strategy," Papers 1206.2934, arXiv.org, revised Aug 2012.
    5. Akahori, Jirô & Fan, Jie Yen & Imamura, Yuri, 2023. "On the convergence order of a binary tree approximation of symmetrized diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 263-277.
    6. Yuji Hishida & Yuta Ishigaki & Toshiki Okumura, 2019. "A Numerical Scheme for Expectations with First Hitting Time to Smooth Boundary," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(4), pages 553-565, December.
    7. Ngo, Hoang-Long & Taguchi, Dai, 2019. "On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 102-112.

    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.

      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:1206.5983. 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.