Generalized Hyperbolic Distributions And Value-At-Risk Estimation For The South African Mining Index

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Chun-Kai Huang
Knowledge Chinhamu
Chun-Sung Huang
Jahvaid Hammujuddy

Keywords

FTSE/JSE Mining Index, Hyperbolic Distribution, Normal-Inverse Gaussian (NIG) Distribution, Generalized Hyperbolic Skew Studentís t-Distribution, Value-at-Risk

Abstract

South Africa is a cornucopia of mineral riches and the performance of its mining industry has significant impacts on the economy. Hence, an accurate distributional assumption of the underlying mining index returns is imperative for the forecasting and understanding of the financial market. In this paper, we propose three subclasses of the generalized hyperbolic distributions as appropriate models for the Johannesburg Stock Exchange (JSE) Mining Index returns. These models are shown to outperform the traditional assumption of normality and accommodate for a number of stylized features, such as excess kurtosis and volatility clustering, embedded within the financial data. The models are compared using the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC) and log-likelihoods. In addition, Value-at-Risk (VaR) estimation and backtesting were also performed to test the extreme tails. The various criteria utilized suggest the generalized hyperbolic (GH) skew Students t-distribution as the most robust model for the South African Mining Index returns.

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