Measuring the error of dynamic hedging: a Laplace transform approach. Computational Finance Vol 12(2

Using the Laplace transform approach, we compute expected value and variance of the error of a hedging strategy for a contingent claim when trading in discrete time. The method applies to a fairly gen-eral 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 improved-delta and the lo-cally risk-minimizing strategy. The formulas obtained are valid for any fixed number of trading dates, whereas all previous results are asymptotic approximations. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.