IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-7643-7794-6_33.html
   My bibliography  Save this book chapter

An Analysis of Asian options

In: Functional Analysis and Evolution Equations

Author

Listed:
  • Jan Prüss

    (Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik)

  • Stefan Sperlich

    (Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik)

  • Mathias Wilke

    (Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik)

Abstract

The objective of this paper is to provide an analytic theory for pricing of Asian options of European type. We present a partial differential equation describing the fair price process of an Asian option. This appears as $$ \left( {\partial _t - A - x \cdot \nabla _y } \right)u = 0 $$ and the associated payoff function as the end value. Here the operator A is the d-dimensional Black-Scholes operator, and B = x·∇ y represents the path dependence in terms of the price averaging in Asian options. The main result will be to prove, that a solution of this partial differential equation exists, is unique, and depends continuously on the data in appropriate function spaces, i.e., that the problem is well posed. On our way we are going to employ semigroup methods, in particular the Lumer-Phillips theorem.

Suggested Citation

  • Jan Prüss & Stefan Sperlich & Mathias Wilke, 2007. "An Analysis of Asian options," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 547-559, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_33
    DOI: 10.1007/978-3-7643-7794-6_33
    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

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:sprchp:978-3-7643-7794-6_33. 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.