A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases

Abstract

We formulate a flexible generalised hyperbolic (GH) option pricing model, which unlike the version proposed by Eberlein and Prause (2002), has all four of its parameters free to be estimated. We also present six three-parameter special cases: a variance gamma (VG), t, hyperbolic, normal inverse Gaussian, reciprocal hyperbolic and normal reciprocal inverse Gaussian option pricing model. Using S&P 500 Index options, we compare the flexible GH, VG, t and Black-Scholes models. The flexible GH model offers the best out-of-sample pricing overall, while the t special case outperforms the VG for both in-sample and out-of-sample pricing. All three models also improve the orthogonality of implied volatility compared to the Black-Scholes model.