Evaluating risk in precious metal prices with generalised lambda, generalised pareto and generalised extreme value distributions

Knowledge Chinhamu; Chun-Kai Huang; Delson Chikobvu

doi:10.37920/sasj.2017.51.1.9

Knowledge Chinhamu School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
Chun-Kai Huang Department of Statistical Sciences, University of Cape Town, Rondebosch, South Africa
Delson Chikobvu Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa

DOI: https://doi.org/10.37920/sasj.2017.51.1.9

Keywords: Expected shortfall, Generalised extreme value, Generalised lambda, Generalised Pareto, Precious metal returns, Value-at-Risk

Abstract

In this study we investigate the performance of the generalised lambda distribution (GLD), the generalised Pareto distribution (GPD) and the generalised extreme value distribution (GEVD) in modelling daily platinum, gold and silver price log-returns. Our primary goal is to compare GLD against GPD, and GEVD, in the estimation of Value-at-Risk (VaR) and expected shortfall (ES) as per the international Basel regulatory framework. Our analyses show that GPD and GLD generally outperform GEVD for VaR and ES estimation for negative precious metal returns. For gold, the GPD stands out as the most suitable model. For platinum, GPD and GLD are equally adequate, especially at the 1% VaR level. For silver, GLD is the most suitable at 1% VaR level, whereas GPD is the best model at 0.1%. This study has shown that GLD is a suitable model for extreme risk in precious metal prices and can be used for the estimation of VaR and ES values.

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