Application of fractional exponential feature to GARCH model variants for improvement in value-at-risk prediction

Abstract

This research studies about using GARCH model variants as a parametric way in estimation and prediction of daily Value-at-Risk (VaR), one of famous risk measurement especially in financial world. To cope with various stylized facts on market's volatility, two mixed GARCH models are proposed in this research: HY-GJR-GARCH model, the hybrid between hyperbolic GARCH (HYGARCH) and GJR-GARCH models, and HY-MS-GARCH model as the amalgam between HYGARCH and Markov switching GARCH (MSGARCH) models. These mixed models, along with rich mathematical formulations and benefits from their base models, are expected that their performance in predicting daily VaR is advanced against the performance of their base models and historical simulations. Using the empirical study of daily S&P 500 index return from 1960 to 1999, all mixed and base models are implemented in fitting data and forward prediction of daily VaR that are compared in various tests. The results indicate dependence of mixed model's performance on market situation that suggested which mixed model and supplementary probability distribution should be used. These results also suggest that the HY-GJR-GARCH mixed model with normal distribution generally advances other models in comparisons, and the HY-MS-GARCH mixed model with Student's t distribution is the most appropriate when a big crisis plunges the market.