Using the Generalized Pareto and Pearson Type-IV Distributions to Measure Value-At-Risk for the Daily South African Mining Index

Risk management tools, such as value-at-risk (VaR) and expected shortfall (conditional value-at-risk) are highly dependent on an appropriate set of underlying distributional assumptions being made. Identifying a distribution that best captures all aspects of financial data sets may benefit both investors and risk managers. In this study, we compare the relative performance of the GARCH-generalized Pareto distribution and the GARCH-Pearson type-IV models in estimating value-at-risk of the South African mining index returns. VaR and backtesting are performed via Kupiec likelihood ratio test. The proposed models capture some key stylized facts associated with daily index returns; e.g. heavy tails (non-normality), asymmetry, volatility clustering and their leverage effect. The advantage of the proposed models lies in their ability to capture conditional heteroscedasticity in the returns through the GARCH framework and at the same time model their heavy tail behaviour through the generalized Pareto distribution (GPD) and the Pearson type-IV distribution. The main findings indicate that the GARCH-GPD and GARCH-Pearson type-IV models give better results when compared with generalized hyperbolic distributions (GHDs), thereby providing a good alternative candidate for modelling financial returns. The accuracy of the volatility model is essential in forecasting volatility of future returns in which the predictability of volatility plays an integral role in risk management and portfolio management.