Measuring the error of dynamic hedging: a Laplace transform approach

Using the Laplace transform approach, we compute the expected value and the variance of the error of a hedging strategy for a contingent claim when trading in discrete time. The method applies to a fairly general class of models, including Black-Scholes, Merton’s jump-diffusion and Normal Inverse Gaussian, and to several interesting strategies, as the Black-Scholes delta, the Wilmott’s improveddelta and the local optimal one. With this approach, also transaction costs may be treated. The results obtained are not asymptotical approximations but exact and efficient formulas, valid for any number of trading dates. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.