Variance-Optimal Hedging for Time-Changed Lévy Processes

Abstract

In this article, we solve the variance-optimal hedging problem in stochastic volatility (SV) models based on time-changed Lévy processes, that is, in the setup of Carr et al. (2003). The solution is derived using results for general affine models in the companion article [Kallsen and Pauwels (2009)].

Key Words:

• Variance-optimal hedging
• Stochastic volatility
• Time-changed Lévy process
• Laplace transform

Acknowledgements

The first author gratefully acknowledges partial support through Sachbeihilfe KA 1682/2-1 of the Deutsche Forschungsgemeinschaft. We sincerely thank Richard Vierthauer and Johannes Muhle-Karbe for their assistance and many discussions. Thanks are also due to two anonymous referees for helpful comments.