Skewness premium with Lévy processes

Abstract

We study the skewness premium (SK) introduced by Bates [J. Finance, 1991, 46(3), 1009-1044] in a general context using Levy processes. Under a symmetry condition, Fajardo and Mordecki [Quant. Finance, 2006, 6(3), 219-227] obtained that SK is given by Bates' x% rule. In this paper, we study SK in the absence of that symmetry condition. More exactly, we derive sufficient conditions for the excess of SK to be positive or negative, in terms of the characteristic triplet of the Levy process under a risk-neutral measure.