Estimation of the value at risk using a long-memory GARCH application to JSE Indices.

Abstract

Financial data are characterized by stylized facts; this makes it difficult to model financial assets if these stylized facts are not taken into account. Therefore, the implementation of accurate risk management tools such as value at risk (VaR), which is crucial in the management of market risk, becomes a futile exercise. This study aims to compare the performance of the long-memory GARCH-type models with heavy-tailed innovations in estimating the value at risk of the All Share Index, the Mining Index, and the Banking Index. This was achieved by investigating the empirical properties of the JSE Indices, fitting the FIGARCH, HYGARCH, and FIAPARCH with the Student’s t-distribution (STD), skewed Student’s t-distribution (SSTD), and generalized error distribution (GED). The study further estimates VaR for the short and long-trading positions on the 95th, 99th, and 99,7th quantiles, as well as backtests the results. The main findings indicate that the JSE All Share index returns is best captured by the FIGARCH-SSTD model, whereas the JSE Mining Index retuns most robust model is the FIAPARCH-STD model. For the JSE Banking Index returns, the FIAPARCH-STD model is predominantly appropriate at most of different VaR levels. The findings of the study provide a solution to both risk practitioners and asset managers for better understanding the behaviour of the financial indices’ returns. Finally, this can assist the role players in fastidiously managing risks and assets’ returns.