IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v17y2014i01ns0219024914500022.html
   My bibliography  Save this article

Volatility Derivatives And Model-Free Implied Leverage

Author

Listed:
  • MASAAKI FUKASAWA

    (Department of Mathematics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka, Japan;
    Center for the Study of Finance and Insurance, Osaka University, Japan)

Abstract

We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black–Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular, we show its simple relation to the Black–Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.

Suggested Citation

  • Masaaki Fukasawa, 2014. "Volatility Derivatives And Model-Free Implied Leverage," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-23.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:01:n:s0219024914500022
    DOI: 10.1142/S0219024914500022
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024914500022
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024914500022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Citations

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


    Cited by:

    1. Peter Friz & Jim Gatheral, 2022. "Diamonds and forward variance models," Papers 2205.03741, arXiv.org.
    2. Elisa Alos & Kenichiro Shiraya, 2017. "Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach," CARF F-Series CARF-F-407, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2018.
    3. Masaaki Fukasawa, 2020. "Volatility has to be rough," Papers 2002.09215, arXiv.org.
    4. Elisa Alòs & Kenichiro Shiraya, 2019. "Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach," Finance and Stochastics, Springer, vol. 23(2), pages 423-447, April.
    5. Tigran Atoyan, 2018. "Model-free trading and hedging with continuous price paths," Papers 1809.00149, arXiv.org, revised Oct 2018.

    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:wsi:ijtafx:v:17:y:2014:i:01:n:s0219024914500022. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.