Several approaches have been considered to model the heavy tails and asymmetric effect on stocks returns volatility. The most commonly used models are the Exponential Generalized Auto-Regressive Conditional Heteroskedasticity (EGARCH), the Threshold GARCH (TGARCH), and the Asymmetric Power ARCH (APARCH) which, in their original form, assume a Gaussian distribution for the innovations. In this paper we propose the estimation of all these asymmetric models on empirical distributions of the Standard & Poor's (S&P) 500 and the Financial Times Stock Exchange (FTSE) 100 daily returns, assuming the Student's t and the stable Paretian (with a < 2) distributions for innovations. To the authors' best knowledge, analysis of the EGARCH and TGARCH assuming innovations with a-stable distribution have not yet been reported in the literature. The results suggest that this kind of distributions clearly outperforms the Gaussian case. However, when a-stable and Student's t distributions are compared, a general conclusion should be avoided as the goodness-of-fit measures favor the astable distribution in the case of S&P 500 returns and the Student's t distribution in the case of FTSE 100.

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EGARCH,TGARCH,Leverage effect,Non-gaussian distributions

• Mechanical Engineering - Engineering and Technology