IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v1y2001i3p318-331.html
   My bibliography  Save this article

Feller processes of normal inverse Gaussian type

Author

Listed:
  • O.E. Barndorff-Nielsen
  • S.Z. Levendorskii

Abstract

We consider the construction of normal inverse Gaussian (NIG) (and some related) Lévy processes from the probabilistic viewpoint and from that of the theory of pseudo-differential operators; we then introduce and analyse natural generalizations of these constructions. The resulting Feller processes are somewhat similar to the NIG Lévy process but may, for instance, possess mean-reverting features. Possible applications to financial mathematics are discussed, and approximations to solutions of corresponding generalizations of the Black-Scholes equation are derived.

Suggested Citation

  • O.E. Barndorff-Nielsen & S.Z. Levendorskii, 2001. "Feller processes of normal inverse Gaussian type," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 318-331, March.
  • Handle: RePEc:taf:quantf:v:1:y:2001:i:3:p:318-331
    DOI: 10.1088/1469-7688/1/3/303
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1088/1469-7688/1/3/303
    Download Restriction: Access to full text is restricted to subscribers.

    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. Alexander Kushpel, 2015. "Pricing of high-dimensional options," Papers 1510.07221, arXiv.org.
    2. repec:wsi:ijtafx:v:20:y:2017:i:05:n:s0219024917500339 is not listed on IDEAS
    3. Lingfei Li & Vadim Linetsky, 2015. "Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach," Finance and Stochastics, Springer, vol. 19(4), pages 941-977, October.
    4. Florian Kleinert & Kees van Schaik, 2013. "A variation of the Canadisation algorithm for the pricing of American options driven by L\'evy processes," Papers 1304.4534, arXiv.org.
    5. Imai Junichi, 2013. "Comparison of random number generators via Fourier transform," Monte Carlo Methods and Applications, De Gruyter, vol. 19(3), pages 237-259, October.
    6. Ole E. Barndorff-Nielsen & Neil Shephard, 2012. "Basics of Levy processes," Economics Papers 2012-W06, Economics Group, Nuffield College, University of Oxford.
    7. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 686-701.
    8. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    9. repec:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2309-y is not listed on IDEAS
    10. Young Kim & Svetlozar Rachev & Michele Bianchi & Frank Fabozzi, 2009. "Computing VAR and AVaR in Infinitely Divisible Distributions," Yale School of Management Working Papers amz2569, Yale School of Management.
    11. Jirô Akahori & Takahiro Tsuchiya, 2006. "What is the Natural Scale for a Lévy Process in Modelling Term Structure of Interest Rates?," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 299-313, December.
    12. Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
    13. Kleinert, Florian & van Schaik, Kees, 2015. "A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3234-3254.
    14. Lin, Zuodong & Rachev, Svetlozar T. & Kim, Young Shin & Fabozzi, Frank J., 2012. "Option pricing with regime switching tempered stable processes," Working Paper Series in Economics 43, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    15. James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    17. Lim, Dongjae & Li, Lingfei & Linetsky, Vadim, 2012. "Evaluating callable and putable bonds: An eigenfunction expansion approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1888-1908.
    18. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.

    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:taf:quantf:v:1:y:2001:i:3:p:318-331. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.