IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v19y2012i5p381-445.html
   My bibliography  Save this article

The Stochastic Intrinsic Currency Volatility Model: A Consistent Framework for Multiple FX Rates and Their Volatilities

Author

Listed:
  • Paul Doust

Abstract

The SABR and the Heston stochastic volatility models are widely used for foreign exchange (FX) option pricing. Although they are able to reproduce the market's volatility smiles and skews for single FX rates, they cannot be extended to model multiple FX rates in a consistent way. This is because when two FX rates with a common currency are described by either SABR or Heston processes, the stochastic process for the third FX rate associated with the three currencies will not be a SABR or a Heston process. A consistent description of the FX market should be symmetric so that all FX rates are described by the same type of stochastic process. This article presents a way of doing that using the concept of intrinsic currency values. To model FX volatility curves, the intrinsic currency framework is extended by allowing the volatility of each intrinsic currency value to be stochastic. This makes the framework more realistic, while preserving all FX market symmetries. The result is a new SABR-style option pricing formula and a model that can simultaneously be calibrated to the volatility smiles of all possible currency pairs under consideration. Consequently, it is more powerful than modelling the volatility curves of each currency pair individually and offers a methodology for comparing the volatility curves of different currency pairs against each other. One potential application of this is in the pricing of FX options, such as vanilla options on less liquid currency pairs. Given the volatilities of less liquid currencies against, for example, USD and EUR, the model could then be used to calculate the volatility smiles of those less liquid currencies against all other currencies.

Suggested Citation

  • Paul Doust, 2012. "The Stochastic Intrinsic Currency Volatility Model: A Consistent Framework for Multiple FX Rates and Their Volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(5), pages 381-445, November.
  • Handle: RePEc:taf:apmtfi:v:19:y:2012:i:5:p:381-445
    DOI: 10.1080/1350486X.2011.626895
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1350486X.2011.626895
    Download Restriction: Access to full text is restricted to subscribers.

    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. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500078 is not listed on IDEAS
    2. Alvise De Col & Alessandro Gnoatto & Martino Grasselli, 2012. "Smiles all around: FX joint calibration in a multi-Heston model," Papers 1201.1782, arXiv.org, revised Jun 2013.
    3. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Options," CARF F-Series CARF-F-290, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197, arXiv.org, revised Feb 2018.
    5. De Col, Alvise & Gnoatto, Alessandro & Grasselli, Martino, 2013. "Smiles all around: FX joint calibration in a multi-Heston model," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3799-3818.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Optionss," CIRJE F-Series CIRJE-F-844, CIRJE, Faculty of Economics, University of Tokyo.

    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:taf:apmtfi:v:19:y:2012:i:5:p:381-445. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.