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

Aleš Černý and Jan Kallsen

Mathematical Finance, 2008, vol. 18, issue 3, 473-492

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.

Date: 2008
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https://doi.org/10.1111/j.1467-9965.2008.00342.x

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