Asymptotic analysis of hedging errors in models with jumps

Peter Tankov (1) , Ekaterina Voltchkova (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 GREMAQ - Groupe de recherche en économie mathématique et quantitative

Most authors who studied the problem of hedging an option 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 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 strategy 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. Theses results are applied to hedging options with discontinuous payoffs in jump-diffusion models.

Mots clés: discrete hedging; weak convergence; Lévy process

Domaines: Probabilités [math.PR]

Peter Tankov, Ekaterina Voltchkova. Asymptotic analysis of hedging errors in models with jumps. 2007. ⟨hal-00186373v1⟩