Errors from discrete hedging in exponential Lévy models: the L2 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.