Mean-Variance Hedging and Optimal Investment in Heston's Model with Correlation

Abstract

This paper solves the mean-variance hedging problem in Heston's model with a stochastic opportunity set moving systematically with the volatility of stock returns. We allow for correlation between stock returns and their volatility (so-called leverage effect).

Our contribution is threefold: using a new concept of opportunity-neutral measure we present a simplified strategy for computing a candidate solution in the correlated case. We then go on to show that this candidate generates the true variance-optimal martingale measure; this step seems to be partially missing in the literature. Finally, we derive formulas for the hedging strategy and the hedging error.

Keywords: mean-variance hedging, stochastic volatility, opportunity-neutral measure, leverage effect, Heston's model, affine process, option pricing, optimal investment

JEL Classification: G11, G12, G13, C61