Mats Broden
Centre for Mathematical Sciences, Lund University

Errors from discrete hedging in exponential Lévy models: the L^2 approach.

Abstract

We analyze the errors arising from discrete rebalancing of the hedging portfolio 
in exponential Lévy models, and establish the rates at which the expected squared 
discretization error goes to zero when the length of the rebalancing step decreases. 
Different hedging strategies and option pay-offs are considered. The case of digital 
options is studied in detail, and it turns out that in this case quadratic hedging 
produces different rates from the usual delta hedging strategy and that for both 
strategies the rates of convergence depend on the Blumenthal-Getoor index of the process.

This is joint work with Peter Tankov.
(preprint at http://people.math.jussieu.fr/~tankov/broden_tankov.pdf)