On the Effect of Skewness and Kurtosis Misspecification on the Hedging Error

Abstract

Using a result in Angelini and Herzel (2009a), we measure, in terms of variance, the cost of hedging a contingent claim when the hedging portfolio is re-balanced at a discrete set of dates. We analyse the dependence of the variance of the hedging error on the skewness and kurtosis as modeled by a Normal Inverse Gaussian model. We consider two types of strategies, the standard Black–Scholes Delta strategy and the locally variance-optimal strategy, and we perform some robustness tests. In particular, we investigate the effect of different types of model misspecification on the performance of the hedging, like that of hedging without taking skewness into account. Computations are performed using a Fast Fourier Transform approach.