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

Mathematical Finance, 2008, 18(3), 473-492

24 Pages Posted: 20 Mar 2008 Last revised: 22 Jun 2020

See all articles by Aleš Černý

Aleš Černý

Business School, City, University of London

Jan Kallsen

Munich University of Technology

Date Written: June 1, 2006

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

Suggested Citation

Černý, Aleš and Kallsen, Jan, Mean-Variance Hedging and Optimal Investment in Heston's Model with Correlation (June 1, 2006). Mathematical Finance, 2008, 18(3), 473-492, Available at SSRN: https://ssrn.com/abstract=909305 or http://dx.doi.org/10.2139/ssrn.909305

Aleš Černý (Contact Author)

Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Jan Kallsen

Munich University of Technology ( email )

Arcisstrasse 21
Munich, DE 80333
Germany

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