Most authors who studied the problem of option hedging in incomplete markets, focused on finding the strategies that minimize the residual hedging error (see, e.g., [1] and [3] ). However, the resulting strategies are usually unrealistic because they require a continuously rebalanced portfolio. In practice, the portfolios are rebalanced discretely, which leads to a ’hedging error of the second type’, due to the difference between the optimal portfolio and its discretely rebalanced version. In this talk, we analyze this second hedging error in the context of exponential L´evy models and give the rates of convergence of the L2 error to zero when the discretization step tends to zero, under different strategies and pay-off profiles. These results extend in particular the work of Gobet and Temam [2] on the hedging of digital options in the diffusion setting.

References

[1] ˇCern´y, A. and Kallsen, J On the Structure of General Mean-Variance Hedging Strategies. The Annals of Probability, 35, no. 4, 1479–1531, (2007).

[2] Gobet, E. and Temam, E. Discrete Time Hedging Errors for Options with Irregular

Pay-offs. Finance and Stochastics, 5, no. 3, 357–367, 2001.

[3] Hubalek, F., Kallsen, J. and Krawczyk, L. Variance-Optimal Hedging for Processes

with Stationary Independent Increments. The Annals of Applied Probability, 16, 853–885, (2006).