Variance Dispersion and Correlation Swaps

Antoine Jacquier () and Saad Slaoui

No 712, Birkbeck Working Papers in Economics and Finance from Birkbeck, Department of Economics, Mathematics & Statistics

Abstract: 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.

JEL-codes: C22 E60 (search for similar items in EconPapers)
Date: 2007-09
New Economics Papers: this item is included in nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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https://eprints.bbk.ac.uk/id/eprint/26900 First version, 2007 (application/pdf)

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Working Paper: Variance dispersion and correlation swaps (2010)
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