MEAN-VARIANCE HEDGING AND OPTIMAL INVESTMENT IN HESTON'S MODEL WITH CORRELATION

Authors: Černý, Aleš¹; Kallsen, Jan²

Source: Mathematical Finance, Volume 18, Number 3, July 2008 , pp. 473-492(20)

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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.

Keywords: mean-variance hedging; stochastic volatility; Heston's model; affine process; option pricing; optimal investment

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9965.2008.00342.x

Affiliations: 1: City University London 2: Christian-Albrechts-Universität zu Kiel

Publication date: 2008-07-01