IDEAS home Printed from
   My bibliography  Save this paper

Swap Rate Variance Swaps


  • Nicolas Merener


We study the hedging and valuation of generalized variance swaps de¯ned on a forward swap interest rate. Our motivation is the fundamental role of variance swaps in the transfer of variance risk, and the extensive empirical evidence documenting that the variance realized by interest rates is stochastic. We identify a hedging rule involving a static European contract and the gains of a dynamic position on forward interest rate swaps. Two distinguishing features arise in the context of interest rates: the nonlinear and multidimensional relationship between the values of the dynamically traded contracts and the underlying swap rate, and the possible stochasticity of the interest rate at which gains are reinvested. The combination of these two features leads to additional terms in the cumulative dynamic trading gains, which depend on realized variance and are taken into consideration in the determination of the appropriate static hedge. We characterize the static payo® function as the solution of an ordinary di®erential equation, and derive explicitly the associated dynamic strategy. We use daily interest rate data between 1997 and 2007 to test the e®ectiveness of our hedging methodology in arithmetic and geometric variance swaps and verify that the hedging error is small compared to the bid-ask spread in swaption prices.

Suggested Citation

  • Nicolas Merener, 2009. "Swap Rate Variance Swaps," Business School Working Papers 2009-02, Universidad Torcuato Di Tella.
  • Handle: RePEc:udt:wpbsdt:2009-02

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Claudio Albanese & Harry Lo & Aleksandar Mijatovic, 2009. "Spectral methods for volatility derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 663-692.
    2. Windcliff, H. & Forsyth, P.A. & Vetzal, K.R., 2006. "Pricing methods and hedging strategies for volatility derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 409-431, February.
    3. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    5. Sam Howison & Avraam Rafailidis & Henrik Rasmussen, 2004. "On the pricing and hedging of volatility derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(4), pages 317-346.
    6. Peter Carr & Hélyette Geman & Dilip Madan & Marc Yor, 2005. "Pricing options on realized variance," Finance and Stochastics, Springer, vol. 9(4), pages 453-475, October.
    7. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    8. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Duyvesteyn, Johan & de Zwart, Gerben, 2015. "Riding the swaption curve," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 57-75.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:udt:wpbsdt:2009-02. 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: (Nicolás Del Ponte) or (Héctor Pastori). General contact details of provider: .

    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 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.

    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.