IDEAS home Printed from https://ideas.repec.org/a/wsi/ijfexx/v02y2015i02ns2424786315500152.html
   My bibliography  Save this article

Local risk-minimization for Lévy markets

Author

Listed:
  • Takuji Arai

    (Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan)

  • Ryoichi Suzuki

    (Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan)

Abstract

In this paper, we aim to obtain explicit representations of locally risk-minimizing by using Malliavin calculus for Lévy processes. For incomplete market models whose asset price is described by a solution to a stochastic differential equation driven by a Lévy process, we derive general formulas of locally risk-minimizing including Malliavin derivatives; and calculate its concrete expressions for call options, Asian options and lookback options.

Suggested Citation

  • Takuji Arai & Ryoichi Suzuki, 2015. "Local risk-minimization for Lévy markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-28.
    • Handle: RePEc:wsi:ijfexx:v:02:y:2015:i:02:n:s2424786315500152
    DOI: 10.1142/S2424786315500152
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S2424786315500152
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S2424786315500152?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.

    Citations

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


    Cited by:

    1. Takuji Arai & Yuto Imai & Ryo Nakashima, 2018. "Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models," Papers 1801.05597, arXiv.org.
    2. Takuji Arai, 2021. "Approximate option pricing formula for Barndorff-Nielsen and Shephard model," Papers 2104.10877, arXiv.org.
    3. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2016. "Numerical Analysis On Local Risk-Minimization For Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-27, March.
    4. Takuji Arai, 2020. "Al\`os type decomposition formula for Barndorff-Nielsen and Shephard model," Papers 2005.07393, arXiv.org, revised Sep 2020.
    5. Takuji Arai, 2019. "Pricing And Hedging Of Vix Options For Barndorff-Nielsen And Shephard Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-26, December.
    6. Takuji Arai & Ryoichi Suzuki, 2019. "A Clark-Ocone type formula via Ito calculus and its application to finance," Papers 1906.06648, arXiv.org.
    7. Takuji Arai, 2019. "Pricing and hedging of VIX options for Barndorff-Nielsen and Shephard models," Papers 1904.12260, arXiv.org.

    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:wsi:ijfexx:v:02:y:2015:i:02:n:s2424786315500152. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/worldscinet/ijfe .

    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.