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We investigate alternative unconditional and conditional distributional models for the returns on Japan's Nikkei 225 stock market index. Among them is the recently introduced class of ARMA-GARCH models driven by α-stable (or stable Paretian) distributed innovations, designed to capture the observed serial dependence, conditional heteroskedasticity and fat-tailedness present in the return data. Of the eight entertained distributions, the partially asymmetric Weibull, Student's t and asymmetric α-stable present themselses as the most viable candidates in terms of overall fit. However, the tails of the sample distribution are approximated best by the asymmetric α-stable distribution. Good tail approximations are particularly important for risk assessments. [ABSTRACT FROM AUTHOR]