Mean-variance hedging and optimal investment in Heston's model with correlation

Černý, A. & Kallsen, J. (2008). Mean-variance hedging and optimal investment in Heston's model with correlation. Mathematical Finance, 18(3), pp. 473-492. doi: 10.1111/j.1467-9965.2008.00342.x

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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.

Item Type: Article
Uncontrolled Keywords: Social Sciences, Science & Technology, Physical Sciences, Business, Finance, Economics, Mathematics, Interdisciplinary Applications, Social Sciences, Mathematical Methods, Business & Economics, Mathematics, Mathematical Methods In Social Sciences, BUSINESS, FINANCE, ECONOMICS, MATHEMATICS, INTERDISCIPLINARY APPLICATIONS, SOCIAL SCIENCES, MATHEMATICAL METHODS, mean-variance hedging, stochastic volatility, Heston's model, affine process, option pricing, optimal investment, STOCHASTIC VOLATILITY, AFFINE PROCESSES, FINANCE
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/3272

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