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Variance Dispersion and Correlation Swaps


  • Antoine Jacquier

    (Department of Economics, Mathematics & Statistics, Birkbeck)

  • Saad Slaoui


In the recent years, banks have sold structured products such as Worst-of options, Everest and Himalayas, resulting in a short correlation exposure. They have hence become interested in offsetting part of this exposure, namely buying back correlation. Two ways have been proposed for such a strategy : either pure correlation swaps or dispersion trades, taking position in an index option and the opposite position in the components options. These dispersion trades have been traded using calls, puts, straddles, and they now trade variance swaps as well as third generation volatility products, namely gamma swaps and barrier variance swaps. When considering a dispersion trade via variance swaps, one immediately sees that it gives a correlation exposure. But it has empirically been showed that the implied correlation - in such a dispersion trade - was not equal to the strike of a correlation swap with the same maturity. Indeed, the implied correlation tends to be around 10 points higher. The purpose of this paper is to theoretically explain such a spread. In fact, we prove that the P&L of a dispersion trade is equal to the sum of the spread between implied and realised correlation - multiplied by an average variance of the components - and a volatility part. Furthermore, this volatility part is of second order, and, more precisely, is of Volga order. Thus the observed correlation spread can be totally explained by the Volga of the dispersion trade. This result is to be reviewed when considering different weighting schemes for the dispersion trade.

Suggested Citation

  • Antoine Jacquier & Saad Slaoui, 2007. "Variance Dispersion and Correlation Swaps," Birkbeck Working Papers in Economics and Finance 0712, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:0712

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    References listed on IDEAS

    1. Brenner, Menachem & Ou, Ernest Y. & Zhang, Jin E., 2006. "Hedging volatility risk," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 811-821, March.
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    1. repec:gam:jrisks:v:5:y:2017:i:4:p:61-:d:119375 is not listed on IDEAS
    2. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024,

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    JEL classification:

    • E60 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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