Measuring the error of dynamic hedging: a Laplace transform approach

Flavio Angelini, Stefano Herzel

Abstract

ABSTRACT

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 general class of models, including Black-Scholes, Merton's jump-diffusion and normal inverse Gaussian, and to several interesting strategies, such as the Black-Scholes delta, the Wilmott's improved-delta and the locally 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 misspecification, to measure the influence of model risk on a hedging strategy.