IDEAS home Printed from https://ideas.repec.org/p/sce/scecf5/471.html
   My bibliography  Save this paper

Wavelet Optimized Finite-Difference Approach to Solve Jump-Diffusion type Partial Differential Equation for Option Pricing

Author

Listed:
  • Mohammad R. Rahman
  • Ruppa K. Thulasiram

    () (Computer Science University of Manitoba)

  • Parimala Thulasiraman

Abstract

The sine and cosine functions used as the bases in Fourier analysis are very smooth (infinitely differentiable) and very broad (nonzero almost everywhere on the real line), and hence they are not effective for representing functions that change abruptly (jumps) or have highly localized support (diffusive). In response to this shortcoming, there has been intense interest in recent years in a new type of basis functions called wavelets. A given wavelet basis is generated from a single function, called a mother wavelet or scaling function, by dilation and translation. By replicating the mother wavelet at many different scales, it is possible to mimic the behavior of any function; this property of wavelets is called multiresolution. Wavelet is a powerful integral transform technique for studying many problems including financial derivatives such as options. Moreover, the approximation error is much smaller than that of the truncated Fourier expansion. Therefore, one can get better approximation of a function at jump discontinuity with the use of wavelet expansion rather than Fourier expansion. In the current study, we employ wavelet analysis to option pricing problem manifested as partial differential equation (PDE) with jump characteristics. We have used wavelets to develop an optimum finite differencing of the differential equations manifested by complex financial models. In particular, we apply wavelet optimized finite-difference (WOFD) technique on the partial differential equation. We describe how Lagrangian polynomial is used to approximate the partial derivatives on an irregular grid. We then describe how to determine sparse and dense grid with wavelets. Further work on implementation is going on.

Suggested Citation

  • Mohammad R. Rahman & Ruppa K. Thulasiram & Parimala Thulasiraman, 2005. "Wavelet Optimized Finite-Difference Approach to Solve Jump-Diffusion type Partial Differential Equation for Option Pricing," Computing in Economics and Finance 2005 471, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:471
    as

    Download full text from publisher

    File URL: http://repec.org/sce2005/up.27738.1108441219.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Courtadon, Georges, 1982. "A More Accurate Finite Difference Approximation for the Valuation of Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(05), pages 697-703, December.
    2. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    options; wavelets; jump-diffusion; finite-difference;

    JEL classification:

    • C - Mathematical and Quantitative Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:sce:scecf5:471. 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: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/sceeeea.html .

    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 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.

    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.