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A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases

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

Abstract

We study a generalised hyperbolic (GH) time-changed Levy process for option pricing and examine six three-parameter special cases: the variance gamma (VG) model of Madan, Carr and Chang (1998), t, hyperbolic, normal inverse Gaussian, reciprocal hyperbolic, and normal reciprocal inverse Gaussian 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 Levy 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 (FMLS) model and the Black-Scholes model. The GH model offers the best in-and out-of-sample performance overall, and the t model special case generally performs better than the better known VG model. We also present a stochastic volatility extension of the GH model.

Suggested Citation

  • Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    • Handle: RePEc:syd:wpaper:2016-14-02
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    References listed on IDEAS

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    2. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.

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    More about this item

    Keywords

    Generalised hyperbolic; T distribution; Variance gamma; Skewness; Levy pro-;
    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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