ABSTRACT
This chapter focuses on discrete mixture models used in finance. It considers finite mixture models and deals with infinite mixture models. The chapter deals with independent and identically distributed mixtures combined with a conditional variance function. Mixture models provide a flexible approach to capture these features of the return distribution. Discrete mixture specifications can be incorporated with volatility dynamics to improve the fit of the conditional distribution. Mixture models have also been incorporated into stochastic volatility specifications. Another area of the financial literature that features discrete mixtures is models of jumps. Countably infinite mixtures are a popular approach in Bayesian nonparametric methods. An infinite mixture model of this form can flexibly represent a wide range of continuous distributions. Mixture modelling appears in many other areas of finance. Applications and extensions of the infinite hidden Markov model have become an active area of research in finance. Mixture models underpin a great deal of research in empirical finance.
