IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-18412-3_17.html
   My bibliography  Save this book chapter

Exotic Derivatives under Stochastic Volatility Models with Jumps

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • Aleksandar Mijatović

    (University of Warwick, Department of Statistics)

  • Martijn Pistorius

    (Imperial College London, Department of Mathematics)

Abstract

In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivatives. We provide closed-form formulae for the Fourier transforms of vanilla and forward starting option prices as well as a formula for the slope of the implied volatility smile for large strikes. A simple explicit approximation formula for the variance swap price is given. The prices of volatility swaps and other volatility derivatives are given as a one-dimensional integral of an explicit function. Analytically tractable formulae for the Laplace transform (in maturity) of the double-no-touch options and the Fourier–Laplace transform (in strike and maturity) of the double knock-out call and put options are obtained. The proof of the latter formulae is based on extended matrix Wiener–Hopf factorisation results. We also provide convergence results.

Suggested Citation

  • Aleksandar Mijatović & Martijn Pistorius, 2011. "Exotic Derivatives under Stochastic Volatility Models with Jumps," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 455-508, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_17
    DOI: 10.1007/978-3-642-18412-3_17
    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:978-3-642-18412-3_17. 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.