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Fitting Generalized Hyperbolic processes - new insights for generating initial values

Author

Listed:
  • Stefan Stöckl

    (ICN Business School, CEREFIGE - Centre Européen de Recherche en Economie Financière et Gestion des Entreprises - UL - Université de Lorraine)

  • Andreas Rathgeber

    (Universität Augsburg [Augsburg])

  • J. Stadler

    (Universität Augsburg [Augsburg])

Abstract

The fitting of Lévy processes is an important field of interest in both option pricing and risk management. In literature, a large number of fitting methods requiring adequate initial values at the start of the optimization procedure exists. A so-called simplified method of moments (SMoM) generates by assuming a symmetric distribution these initial values for the Variance Gamma process, whereby the idea behind can be easily transferred to the Normal Inverse Gaussian process. However, the characteristics of the Generalized Hyperbolic process prevent such an easy adaption. Therefore, we provide by applying a Taylor series approximation for the modified Bessel function of the third kind, a Tschirnhaus transformation and a symmetric distribution assumption, a SMOM for the Generalized Hyperbolic distribution. Our simulation study compares the results of our SMoM with the results of the maximum likelihood estimation. The results show that our proposed approach is an appropriate and useful way for estimating Generalized Hyperbolic process parameters and significantly reduces estimation time.

Suggested Citation

  • Stefan Stöckl & Andreas Rathgeber & J. Stadler, 2017. "Fitting Generalized Hyperbolic processes - new insights for generating initial values," Post-Print hal-01768898, HAL.
    • Handle: RePEc:hal:journl:hal-01768898
    DOI: 10.1080/03610918.2016.1175624
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    Cited by:

    1. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.

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