Premium
Empirical Analyses of Extreme Value Models for the S outh A frican M ining I ndex
Author(s) -
Chinhamu Knowledge,
Huang ChunKai,
Huang ChunSung,
Hammujuddy Jahvaid
Publication year - 2015
Publication title -
south african journal of economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.502
H-Index - 31
eISSN - 1813-6982
pISSN - 0038-2280
DOI - 10.1111/saje.12051
Subject(s) - kurtosis , extreme value theory , econometrics , generalized extreme value distribution , maxima , value at risk , mathematics , statistics , value (mathematics) , generalized pareto distribution , economics , finance , art , performance art , art history , risk management
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 J ohannesburg Stock E xchange M ining I ndex 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.