Hedging (Co)Variance Risk with Variance Swaps

Abstract

In this paper we introduce a new criterion in order to measure the variance and covariance risks in financial markets. Unlike past literature, we quantify the (co)variance risk by comparing the spread between the initial wealths required to obtain the same final utility in an incomplete and completed market case. We provide explicit solutions for both cases in a stochastic correlation framework where the market is completed by introducing volatility products, namely Variance Swaps. Using real data on major indexes, we find that this criterion provides a better measure of the market risks with respect to the (misleading) traditional approach based on the hedging demand.

Keywords: Wishart Affine Stochastic Correlation model, complete and incomplete markets, variance swaps, optimal portfolio choice

JEL Classification: G11, G12