Option pricing under non-normality: a comparative analysis

This paper carries out a comparative analysis of the calibration and performance of a variety of options pricing models. These include Black and Scholes (J Polit Econ 81:637–659, <CitationRef CitationID="CR6">1973</CitationRef>), the Gram–Charlier (GC) approach of Backus et al. (<CitationRef CitationID="CR4">1997</CitationRef>), the stochastic volatility (HS) model of Heston (Rev Financ Stud 6:327–343, <CitationRef CitationID="CR21">1993</CitationRef>), the closed-form GARCH process of Heston and Nandi (Rev Financ Stud 13:585–625, <CitationRef CitationID="CR22">2000</CitationRef>) and a variety of Lévy processes including the Variance Gamma (VG), Normal Inverse Gaussian (NIG), and, CGMY and Kou (Manag Sci 48:1086–1101, <CitationRef CitationID="CR25">2002</CitationRef>) jump-diffusion models. Unlike most studies of option pricing, we compare these models using a common point-in-time data which reflects the perspective of a new investor who wishes to choose between models using only the most minimal recent data set. For each of these models, we also examine the accuracy of delta and delta-gamma approximations to the valuation of both individual options and an illustrative option portfolio. Copyright Springer Science+Business Media, LLC 2013