Journal of Statistics Applications & Probability


It is essential for financial institutions and regulators to implement an effective risk management system against market risk. Value-at-Risk (VaR) is the most popular tool to measure such risk. It is thus important to model the volatility of precious metal prices and develop more robust approaches in the estimation of VaR. There is a gap in literature in terms of VaR models that can capture all the empirical properties of precious metals. The main aim of the study was to propose a modelling framework using Long memory models coupled with normal-inverse Gaussian (NIG), the variance-gamma (VG) and the Pearson type-IV (PIV) distributions which can be used in precious metal market for carrying out accurate risk management or assessment. In this study, we evaluate the relative performances of long memory (LM) generalized autoregressive conditional heteroscedasticity (GARCH) models, under a number of conditional assumptions, in estimating VaR for daily returns from three precious metal (platinum, gold, silver) prices. Such models aim at jointly capturing the volatility clustering, unconditional and conditional heavy-tailed, asymmetrical distributions and LM inherent in the data series. In particular, the conditional variance and LM are modeled by nonlinear GARCH models, while the NIG, the VG and the PIV distributions are applied to the extracted standardized residuals so as to capture the heavy tail behavior in metal returns. Anderson- Darling (AD) test is utilized to check for model adequacy while Kupiec likelihood ratio test is used in this study to objectively compare relative performances of the VaR models. The backtesting results confirm that the LM GARCH-heavy-tailed distribution models are adequate methods in improving risk management assessments and hedging strategies in the highly volatile metals market. The main findings indicate that ARFIMA-FIGARCH, ARFIMA-HYGARCH and ARFIMA-FIAPARCH models with PIV, VG and NIG error distributions are suitable for depicting the extreme risk of precious metal prices and can be used for the estimation of VaR. 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.

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