Skewing Up Correlation: Understanding Correlation Skew in Equity Derivatives

Abstract

The goal of this paper is to fill in the gap between the multi-asset equity derivatives market and the mathematical models developed to treat the correlation skew problem. We analyze the structure of the equity correlation market and explain which parts are affected by correlation skew. Using a Jacobi instantaneous correlation model as a vehicle to gain intuition, we approach the issue from both the perspective of historical realized correlation as well as from the market-implied one. We study the effect of correlation skew on the typical structures traded in the correlation market. The main result is the calibration procedure for such a model. Once calibrated, the model provides a link between various correlation derivatives, most importantly between the basket dispersion trades and Worst-Of structures, the two main vehicles of correlation business.

Keywords: correlation skew, stochastic correlation, Jacobi process, index skew, implied correlation

JEL Classification: G13