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A Flexible Generalized Hyperbolic Option Pricing Model and Its Special Cases

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  • Claudia Yeap
  • Simon S Kwok
  • S T Boris Choy

Abstract

We study a generalized hyperbolic (GH) time-changed Lévy process for option pricing and examine six three-parameter special cases: the variance gamma (VG) model of Madan, Carr, and Chang (1998), t, hyperbolic (H), normal inverse Gaussian (NIG), reciprocal hyperbolic (RH), and normal reciprocal inverse Gaussian (NRIG) option pricing models. We study the GH model’s moment properties of the associated risk-neutral distribution of logarithmic spot returns, and obtain an explicit pricing formula for European options facilitated by the time-change Lévy process construction. Using S&P 500 Index European options during low and high volatility sample periods, we compare the GH model empirically with existing benchmark models such as the finite-moment log-stable model and the Black–Scholes model. The GH model offers the best in- and out-of-sample performance overall, and a proposed t model special case generally outperforms the existing VG special case. We also present a stochastic volatility extension of the GH model.

Suggested Citation

  • Claudia Yeap & Simon S Kwok & S T Boris Choy, 2018. "A Flexible Generalized Hyperbolic Option Pricing Model and Its Special Cases," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 425-460.
    • Handle: RePEc:oup:jfinec:v:16:y:2018:i:3:p:425-460.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbx030
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    More about this item

    Keywords

    generalized hyperbolic; Lévy processes; t distribution; time deformation; variance gamma;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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