IDEAS home Printed from https://ideas.repec.org/h/wsi/wschap/9789812812599_0011.html
   My bibliography  Save this book chapter

E-Arch Model For Implied Volatility Term Structure Of Fx Options

In: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar

Author

Listed:
  • YINGZI ZHU

    (Citibank, N.A., 909 Third Avenue, 29th Floor, Zone 1, New York, NY 10043, USA)

  • MARCO AVELLANEDA

    (Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA)

Abstract

We construct a statistical model for term structure of implied volatility of currency options based on daily historical data for 13 currency pairs in a 19-month period. We examine the joint evolution of 1 month, 2 month, 3 month, 6 month and 1 year 50 Δ options in all the currency pairs. We show that from these five observable variables, there exist three uncorrelated state variables (principal components) which account for the parallel movement, slope oscillation, and curvature of the term structure and which explain, on average, the movements of the term structure of volatility to more than 95% in all cases. We test and construct an exponential ARCH, or E-ARCH, model for each state variable. One of the applications of this model is to produce confidence bands for the term structure of volatility.

Suggested Citation

  • Yingzi Zhu & Marco Avellaneda, 1999. "E-Arch Model For Implied Volatility Term Structure Of Fx Options," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 11, pages 271-291, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812812599_0011
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/pdf/10.1142/9789812812599_0011
    Download Restriction: Ebook Access is available upon purchase.
    File URL: https://www.worldscientific.com/doi/abs/10.1142/9789812812599_0011
    Download Restriction: Ebook Access is available upon purchase.
    ---><---

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

    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:wsi:wschap:9789812812599_0011. 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.worldscientific.com/page/worldscibooks .

    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.