Short Option Maturity Term Structures of Skewness and Excess Kurtosis

Abstract

Absolute skewness and excess kurtosis are observed to increase with maturity for short maturity options in contrast to the result for the longer maturities. Lévy and Sato processes are not consistent with this behavior. Neither are additive processes obtained by arbitrary time changes and space scalings applied to an underlying Lévy process. Additive processes with bilateral gamma marginals along with separate space scalings and time changes applied to the up and down moves are observed to deliver such term structures. The two sided CGMY model with infinite variation on the up side and finite variation down deliver term structure results qualitatively similar to that of the raw data on skewness and excess kurtosis. However, this model falls short in the quantitative magnitudes for maturity elasticities of absolute skewness and excess kurtosis.

Keywords: Bilateral Gamma, CGMY model, Additive Processes, Space Scaled and Time Changed Lévy Processes.

JEL Classification: G10, G11, G12.