| Summary: | 碩士 === 國立高雄應用科技大學 === 金融資訊研究所 === 99 === Empirical studies based on GARCH models show that the hypothesis that the distribution of residuals is normally distributed is often rejected (e.g., Duan, 1999; Menn and Rachev, 2009; Kim et al., 2010). Hence, most of the recent literature consider non-normal stock price models (e.g., Rachev et al., 2007; Fusai and Meucci, 2008; Farinelli et al., 2008; Sorwar and Dowd, forthcoming). Duan et al. (2006) enhance the classical GARCH model by adding jumps to the innovation process. This paper attempts to forecast both extreme events and highly volatile markets. We use in predicting real-world market crashed, such as Black Monday (October 19, 1987), the global economic meltdown attributable to the subprime mortgage meltdown in 2007 and the Lehman Brothers failure in the latter half year of 2008. Due to the properties of skewness, leptokurtosis, fat tails as well as the time varying volatility of ARMA-GARCH model with standard Lévy process, we compute VaR and AVaR and then develop early warning system and fear index based on ARMA-GARCH model with standard Lévy process. Empirical study, estimating VaR and AVaR for ARMA-GARCH model with standard Lévy process can be regarded as a suitable early warning system and the fear index, especially in the larger volatility clustering events of the FTSE, the HSI, the Nikkei 225, the DJIA, the NYSE, and the SPX.
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