Variance Dispersion and Correlation Swaps

14 Pages Posted: 8 Jul 2007 Last revised: 17 Feb 2010

See all articles by Antoine (Jack) Jacquier

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

SAAD SLAOUI

affiliation not provided to SSRN

Date Written: July 1, 2007

Abstract

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.

Keywords: Variance Swaps, Gamma Swaps, Correlation Swaps, dispersion trades

JEL Classification: G12

Suggested Citation

Jacquier, Antoine and SLAOUI, SAAD, Variance Dispersion and Correlation Swaps (July 1, 2007). Available at SSRN: https://ssrn.com/abstract=998924 or http://dx.doi.org/10.2139/ssrn.998924

Antoine Jacquier (Contact Author)

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

SAAD SLAOUI

affiliation not provided to SSRN ( email )

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