IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/272.html
   My bibliography  Save this paper

Option Valuation in Multivariate SABR Models

Author

Listed:
  • Jörg Kienitz

    (Deutsche Postbank AG)

  • Manuel Wittke

    (University of Bonn)

Abstract

We consider the joint dynamic of a basket of n-assets where each asset itself follows a SABR stochastic volatility model. Using the Markovian Projection methodology we approximate a univariate displaced diffusion SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but also the skew, the cross-skew and the decorrelation in our approximation. The latter is not possible in alternative approximations to price e.g. spread options. We illustrate the method by considering the example where the underlyings are two constant maturity swap (CMS) rates. Here we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach.

Suggested Citation

  • Jörg Kienitz & Manuel Wittke, 2010. "Option Valuation in Multivariate SABR Models," Research Paper Series 272, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:272
    as

    Download full text from publisher

    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp272.pdf
    Download Restriction: no

    Citations

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


    Cited by:

    1. Cyril Grunspan, 2011. "A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1782, arXiv.org.

    More about this item

    Keywords

    SABR; CMS spread; displaced diffusion; Markovian projection; Gyongy Lemma;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:uts:rpaper:272. 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: (Duncan Ford). General contact details of provider: http://edirc.repec.org/data/qfutsau.html .

    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.