Empirical Analyses of Extreme Value Models for the South African Mining Index |
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| Authors: | Knowledge Chinhamu Chun‐Kai Huang Chun‐Sung Huang Jahvaid Hammujuddy |
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| Affiliation: | 1. School of Mathematics, Statistics and Computer Science, University of KwaZulu‐Natal, Westville, Durban, KZN, South Africa;2. Department of Statistical SciencesUniversity of Cape Town;3. Department of Finance and TaxUniversity of Cape Town;4. School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu‐Natal |
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| Abstract: | While the classical normality assumption is simple to implement, it is well known to underestimate the leptokurtic behaviour demonstrated in most financial data. After examining properties of the Johannesburg Stock Exchange Mining Index returns, we propose two extreme value models to fit its negative tail with a higher degree of accuracy. The generalised extreme value distribution (GEVD) is fitted using the block maxima approach, while the generalised Pareto distribution (GPD) is fitted using the peaks‐over‐threshold method. Numerical assessment of value‐at‐risk (VaR) estimates indicates that both GEVD and GPD increasingly outperform the normal distribution as we move further into the lower tail. In addition, GEVD produces lower estimates relative to that of the historical VaR, and GPD provides slightly more conservative estimates for adequate capitalisation. |
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| Keywords: | C52 C53 G17 FTSE/JSE Mining Index generalised extreme value distribution generalised Pareto distribution value‐at‐risk Kupiec likelihood ratio test |
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