IDEAS home Printed from https://ideas.repec.org/a/kap/apfinm/v22y2015i2p185-207.html
   My bibliography  Save this article

An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space

Author

Listed:
  • Kazuhiro Yoshikawa

Abstract

In this paper, we show that every antisymmetric multiple stochastic (Ito’s) integral has a polynomial form of single and double ones. As an application, a new approximating scheme for the solution to a stochastic differential equation is proposed. Copyright Springer Japan 2015

Suggested Citation

  • Kazuhiro Yoshikawa, 2015. "An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 185-207, May.
    • Handle: RePEc:kap:apfinm:v:22:y:2015:i:2:p:185-207
    DOI: 10.1007/s10690-014-9199-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10690-014-9199-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10690-014-9199-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
    2. Shigeo Kusuoka & Syoiti Ninomiya, 2004. "A New Simulation Method of Diffusion Processes Applied to Finance," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 11, pages 233-253, World Scientific Publishing Co. Pte. Ltd..
    3. Mariko Ninomiya & Syoiti Ninomiya, 2009. "A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method," Finance and Stochastics, Springer, vol. 13(3), pages 415-443, September.
    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. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(2), pages 147-182, May.
    2. Akiyama, Naho & Yamada, Toshihiro, 2024. "A weak approximation for Bismut’s formula: An algorithmic differentiation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 386-396.
    3. Yusuke Morimoto & Makiko Sasada, 2015. "Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications," Papers 1510.02013, arXiv.org, revised Dec 2015.
    4. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
    5. Denis Belomestny & Tigran Nagapetyan, 2014. "Multilevel path simulation for weak approximation schemes," Papers 1406.2581, arXiv.org, revised Oct 2014.
    6. Aur'elien Alfonsi & Edoardo Lombardo, 2022. "High order approximations of the Cox-Ingersoll-Ross process semigroup using random grids," Papers 2209.13334, arXiv.org, revised Apr 2023.
    7. Christian Bayer & Peter Friz & Ronnie Loeffen, 2010. "Semi-Closed Form Cubature and Applications to Financial Diffusion Models," Papers 1009.4818, arXiv.org.
    8. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
    9. Rey, Clément, 2019. "Approximation of Markov semigroups in total variation distance under an irregular setting: An application to the CIR process," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 539-571.
    10. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Post-Print hal-00491371, HAL.
    11. Christian Bayer & Peter K. Friz, 2013. "Cubature on Wiener space: pathwise convergence," Papers 1304.4623, arXiv.org.
    12. Abdelkoddousse Ahdida & Aur'elien Alfonsi, 2011. "A Mean-Reverting SDE on Correlation matrices," Papers 1108.5264, arXiv.org, revised Feb 2012.
    13. Mariko Ninomiya, 2011. "Sde Weak Approximation Library (Sde Wa) (Version 1.0)," CARF F-Series CARF-F-274, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    14. Christian Bayer & Peter Friz & Ronnie Loeffen, 2012. "Semi-closed form cubature and applications to financial diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 13(5), pages 769-782, October.
    15. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de opciones call asiáticas Promedio Aritmético usando Taylor Estocástico 1.5," Working Papers 44, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
    16. Hocquet, Antoine & Vogler, Alexander, 2023. "An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 183-217.
    17. Christian Bayer & Peter K. Friz & Paul Gassiat & Joerg Martin & Benjamin Stemper, 2017. "A regularity structure for rough volatility," Papers 1710.07481, arXiv.org.
    18. Al Gerbi, A. & Jourdain, B. & Clément, E., 2018. "Asymptotics for the normalized error of the Ninomiya–Victoir scheme," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1889-1928.
    19. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-682, CIRJE, Faculty of Economics, University of Tokyo.
    20. Arturo Kohatsu-Higa & Salvador Ortiz-Latorre & Peter Tankov, 2012. "Optimal simulation schemes for L\'evy driven stochastic differential equations," Papers 1204.4877, arXiv.org.

    More about this item

    Keywords

    Stochastic area; Numerical analysis of stochastic differential equation; Fermion Fock space; G13;
    All these keywords.

    JEL classification:

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

    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:kap:apfinm:v:22:y:2015:i:2:p:185-207. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.