Advanced Search
MyIDEAS: Login to save this paper or follow this series

Option Pricing with Lie Symmetry Analysis and Similarity Reduction Method

Contents:

Author Info

  • Wenqing Bao
  • ChunLi Chen
  • Jin E. Zhang
Registered author(s):

    Abstract

    With some transformations, we convert the problem of option pricing under state-dependent volatility into an initial value problem of the Fokker-Planck equation with a certain potential. By using the Lie symmetry analysis and similarity reduction method, we are able to reduce the dimensions of the partial differential equation and find some of its particular solutions of the equation. A few case studies demonstrate that our new method can be used to produce analytical option pricing formulas for certain volatility functions.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://arxiv.org/pdf/1311.4074
    File Function: Latest version
    Download Restriction: no

    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1311.4074.

    as in new window
    Length:
    Date of creation: Nov 2013
    Date of revision:
    Handle: RePEc:arx:papers:1311.4074

    Contact details of provider:
    Web page: http://arxiv.org/

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 145-166.
    2. C. F. Lo & C. H. Hui, 2001. "Valuation of financial derivatives with time-dependent parameters: Lie-algebraic approach," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(1), pages 73-78.
    3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    5. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    6. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, American Finance Association, vol. 44(1), pages 211-19, March.
    7. Peter Laurence & Tai-Ho Wang, 2005. "Closed Form Solutions For Quadratic And Inverse Quadratic Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1059-1083.
    8. Jin E. Zhang & Yishen Li, 2012. "New analytical option pricing models with Weyl--Titchmarsh theory," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 12(7), pages 1003-1010, June.
    9. Yishen Li & Jin Zhang, 2004. "Option pricing with Weyl-Titchmarsh theory," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 4(4), pages 457-464.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:arx:papers:1311.4074. 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: (arXiv administrators).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.