Asymptotic Analysis of Hedging Errors in Models with Jumps

Most authors who studied the problem of option hedging in incomplete markets, and, in particular, in models with jumps, focused on finding the strategies that minimize the residual hedging error. However, the resulting strategies are usually unrealistic because they require a continuously rebalanced portfolio, which is impossible to achieve in practice due to transaction costs. In reality, 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 paper, we analyze this second hedging error and establish a limit theorem for the renormalized error, when the discretization step tends to zero, in the framework of general Itô processes with jumps. The results are applied to the problem of hedging an option with a discontinuous pay-off in a jump-diffusion model