A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns

We discuss the calibration of the univariate and multivariate generalized hyperbolic distributions, as well as their hyperbolic, variance gamma, normal inverse Gaussian, and skew Student’s t-distribution subclasses for the daily log-returns of seven of the most liquid mining stocks listed on the Joh...

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Main Authors: Virginie Konlack Socgnia, Diane Wilcox
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/263465
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author Virginie Konlack Socgnia
Diane Wilcox
author_facet Virginie Konlack Socgnia
Diane Wilcox
author_sort Virginie Konlack Socgnia
collection DOAJ
description We discuss the calibration of the univariate and multivariate generalized hyperbolic distributions, as well as their hyperbolic, variance gamma, normal inverse Gaussian, and skew Student’s t-distribution subclasses for the daily log-returns of seven of the most liquid mining stocks listed on the Johannesburg Stocks Exchange. To estimate the model parameters from historic distributions, we use an expectation maximization based algorithm for the univariate case and a multicycle expectation conditional maximization estimation algorithm for the multivariate case. We assess the goodness of fit statistics using the log-likelihood, the Akaike information criterion, and the Kolmogorov-Smirnov distance. Finally, we inspect the temporal stability of parameters and note implications as criteria for distinguishing between models. To better understand the dependence structure of the stocks, we fit the MGHD and subclasses to both the stock returns and the two leading principal components derived from the price data. While the MGHD could fit both data subsets, we observed that the multivariate normality of the stock return residuals, computed by removing shared components, suggests that the departure from normality can be explained by the structure in the common factors.
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spelling doaj-art-35aee73b9108425d8e0943eeaec5e2022025-08-20T03:55:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/263465263465A Comparison of Generalized Hyperbolic Distribution Models for Equity ReturnsVirginie Konlack Socgnia0Diane Wilcox1School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag X3, Wits 2050, South AfricaSchool of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag X3, Wits 2050, South AfricaWe discuss the calibration of the univariate and multivariate generalized hyperbolic distributions, as well as their hyperbolic, variance gamma, normal inverse Gaussian, and skew Student’s t-distribution subclasses for the daily log-returns of seven of the most liquid mining stocks listed on the Johannesburg Stocks Exchange. To estimate the model parameters from historic distributions, we use an expectation maximization based algorithm for the univariate case and a multicycle expectation conditional maximization estimation algorithm for the multivariate case. We assess the goodness of fit statistics using the log-likelihood, the Akaike information criterion, and the Kolmogorov-Smirnov distance. Finally, we inspect the temporal stability of parameters and note implications as criteria for distinguishing between models. To better understand the dependence structure of the stocks, we fit the MGHD and subclasses to both the stock returns and the two leading principal components derived from the price data. While the MGHD could fit both data subsets, we observed that the multivariate normality of the stock return residuals, computed by removing shared components, suggests that the departure from normality can be explained by the structure in the common factors.http://dx.doi.org/10.1155/2014/263465
spellingShingle Virginie Konlack Socgnia
Diane Wilcox
A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
Journal of Applied Mathematics
title A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
title_full A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
title_fullStr A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
title_full_unstemmed A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
title_short A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
title_sort comparison of generalized hyperbolic distribution models for equity returns
url http://dx.doi.org/10.1155/2014/263465
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