Variance dispersion and correlation swaps

TL;DR

This paper provides a theoretical explanation for the correlation spread observed in dispersion trades using variance swaps, linking it to the volga of the trade and clarifying the relationship between implied and realized correlation.

Contribution

It offers a mathematical model showing that the correlation spread in dispersion trades is driven by the volga of the position, enhancing understanding of correlation risk management.

Findings

Correlation spread is explained by the volga of dispersion trades.

The P&L of dispersion trades decomposes into implied-realized correlation spread and volatility effects.

Volga order effects are significant in the correlation spread analysis.

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 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.