Work

The Generalized Hyperbolic Distribution Family: A Unified Review and an Empirical Comparison of Nested Models for Financial Returns

Year: 2026

Type: article

Abstract: This study provides a unified theoretical and empirical examination of the Generalized Hyperbolic (GH) distribution family. The special and limiting relationships among the GH distribution and its important subclasses are reviewed. The empirical analysis considers daily returns on the SPDR S&P 500 ETF Trust (SPY) from 4 January 2010 to 22 July 2024. The unrestricted GH distribution and its subclasses—Variance Gamma (VG), Normal Inverse Gaussian (NIG), Normal Reciprocal Inverse Gaussian (NRIG), Hyperbolic (H), Reciprocal Hyperbolic (RH) and Hyperbola (HA)—are estimated via the maximum likelihood method. Overall, the results demonstrate that the GH family provides a flexible and effective alternative to the Gaussian benchmark, although the preferred subclass depends on whether predictive adequacy or model parsimony is emphasized.

Source: Mathematical and Computational Applications

DOI: 10.3390/mca31050231

Authors: Aubain Nzokem, Daniel Maposa, Saheed Akindeinde

Institutions: Copper Mountain College, University of Limpopo, Botswana International University of Science and Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,689

OpenAlex ID: W7222701982

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