The Generalized Hyperbolic Distribution

Michele Leonardo Bianchi, Stoyan V Stoyanov, Gian Luca Tassinari, Frank Fabozzi () and Sergio M Focardi

Chapter 4 in Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management, 2019, pp 109-148 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The main topics covered in this chapter are:the definition and the main properties of the class of generalized hyperbolic distributions including different parameterizations, tail behavior, and central and non-central moments common in applications in finance;special subclasses which represent popular models in finance including the hyperbolic, the normal inverse Gaussian, the hyperbolic skewed t, the variance gamma, and other distributions;a random number generator for the general case and the most important subclasses;the method of maximum likelihood for parameter estimation for the general case and the most important subclasses;an empirical comparison of the fits of the generalized hyperbolic class and the most important subclasses based on the daily returns of the S&P500 and Nikkei 225 indices;the intuition behind the multivariate generalized hyperbolic distribution.

Keywords: Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2019
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