IDEAS home Printed from https://ideas.repec.org/h/spr/sprfcp/978-3-540-47856-0_6.html

The Itô Formula

In: A Benchmark Approach to Quantitative Finance

Author

Listed:
  • Eckhard Platen

    (University of Technology)

  • David Heath

    (Australian National University)

Abstract

The price of a security, for instance, a zero coupon bond which generates some future payoff at a maturity date, is often dependent on the value of an underlying process. In many applications, the effect of changes in the underlying process on this price needs to be quantified. In deterministic calculus this type of problem is handled by the chain rule. In stochastic calculus the corresponding generalization of the chain rule is given by the Itô formula. This stochastic chain rule contains terms reflecting the effect due to the stochastic processes involved having non-zero quadratic variation. In this chapter we introduce, apply and derive the Itô formula. It is widely regarded as the main tool in stochastic calculus and is therefore highly important in quantitative finance.

Suggested Citation

  • Eckhard Platen & David Heath, 2006. "The Itô Formula," Springer Finance, in: A Benchmark Approach to Quantitative Finance, chapter 6, pages 205-235, Springer.
    • Handle: RePEc:spr:sprfcp:978-3-540-47856-0_6
    DOI: 10.1007/978-3-540-47856-0_6
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprfcp:978-3-540-47856-0_6. 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: 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.