Postprint version. Published in Journal of Financial Economics, Volume 85, September 1, 2007, pages 822-856.
NOTE: At the time of publication, the author Garland Durham was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1016/j.jfineco.2006.06.005.
Understanding both the dynamics of volatility and the shape of the distribution of returns conditional on the volatility state is important for many financial applications. A simple single-factor stochastic volatility model appears to be sufficient to capture most of the dynamics. It is the shape of the conditional distribution that is the problem. This paper examines the idea of modeling this distribution as a discrete mixture of normals. The flexibility of this class of distributions provides a transparent look into the tails of the returns distribution. Model diagnostics suggest that the model, SV-mix, does a good job of capturing the salient features of the data. In a direct comparison against several affine-jump models, SV-mix is strongly preferred by Akaike and Schwarz information criteria.