IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i2p173-178.html
   My bibliography  Save this article

A note on the Malliavin derivative operator under change of variable

Author

Listed:
  • Ewald, Christian-Oliver

Abstract

The Malliavin derivative operator is classically defined with respect to the standard Brownian motion on the Wiener space C0[0,T]. We define the Malliavin derivative with respect to arbitrary Brownian motions on general probability spaces and compute how the Malliavin derivative of a functional on the Wiener space changes when the functional is composed with transformation by a process which is sufficiently smooth. We then use this result to derive a formula which says how the Malliavin derivatives with respect to different Brownian motions on the same state space are related to each other. This has applications in many situations in Mathematical Finance, where Malliavin calculus is used.

Suggested Citation

  • Ewald, Christian-Oliver, 2008. "A note on the Malliavin derivative operator under change of variable," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 173-178, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:2:p:173-178
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00210-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Christian-Oliver Ewald & Aihua Zhang, 2006. "A new technique for calibrating stochastic volatility models: the Malliavin gradient method," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 147-158.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Elisa Alòs & Thorsten Rheinländer, 2015. "Pricing and hedging Margrabe options with stochastic volatilities," Economics Working Papers 1475, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2017.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Elisa Alòs & Christian-Olivier Ewald, 2005. "A note on the Malliavin differentiability of the Heston volatility," Economics Working Papers 880, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Christian-Oliver Ewald & Zhaojun Yang, 2008. "Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 97-123, August.
    3. Bilgi Yilmaz, 2018. "Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus," Papers 1806.06061, arXiv.org.
    4. Yang, Zhaojun & Ewald, Christian-Oliver, 2010. "On the non-equilibrium density of geometric mean reversion," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 608-611, April.

    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:eee:stapro:v:78:y:2008:i:2:p:173-178. 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.

    If CitEc recognized a bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.