Variance dispersion and correlation swaps
AbstractIn 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 set up using calls, puts, straddles, variance swaps as well as third generation volatility products. When considering a dispersion trade using variance swaps, one immediately sees that it gives a correlation exposure. Empirical analysis have showed that this implied correlation was not equal to the strike of a correlation swap with the same maturity. 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1004.0125.
Date of creation: Apr 2010
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Web page: http://arxiv.org/
Other versions of this item:
- Antoine Jacquier & Saad Slaoui, 2007. "Variance Dispersion and Correlation Swaps," Birkbeck Working Papers in Economics and Finance, Birkbeck, Department of Economics, Mathematics & Statistics 0712, Birkbeck, Department of Economics, Mathematics & Statistics.
- 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 &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-11 (All new papers)
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- Brenner, Menachem & Ou, Ernest Y. & Zhang, Jin E., 2006. "Hedging volatility risk," Journal of Banking & Finance, Elsevier, Elsevier, vol. 30(3), pages 811-821, March.
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