Modelling heavy tails and asymmetry using ARCH-type models with stable Paretian distributions

Abstract

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 AutoRegressive 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 (α < 2) distributions for innovations. To the authors’ best knowledge, analysis of the EGARCH and TGARCH assuming innovations with α-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 α-stable and Student’s t distributions are compared, a general conclusion should be avoided as the goodness-of-fit measures favor the α-stable distribution in the case of S&P 500 returns and the Student’s t distribution in the case of FTSE 100.