Two essays in Markov mixture of normals approach to modeling financial returns

Financial asset returns often exhibit time-varying conditional distributions, departures from normality, and persistence in volatility. Higher moments of financial returns distribution are especially important in applications in which tail probability is of major interest or concern. Markov mixture of distributions allows for both temporal dependence and stochastic variation in the moments. Markov mixtures models are capable of handling nearly any feature of the unconditional distribution including leptokurtosis and skewness.; This paper adopts the full Bayesian estimation approach based on the method of Gibbs sampling, and the latent state variables simulation algorithm (Gibb sampling-data augmentation (GS-DA)) to estimate the Markov mixture of normals model. Using daily returns from the S&P 500 index, formal model comparisons are conducted to examine the performance of the Markov mixture structures relative to two well-known alternatives, the GARCH and the t-GARCH models. In addition, predictive decompositions of the marginal likelihoods are analyzed to help identify specific episodes that highlight the differences in the models. The results clearly indicate that Markov mixtures of normals models are viable, if not superior, alternatives to modeling financial returns.; The idea that risk aversion may vary over time with the state of the economy is not new. Time-varying risk aversion can explain the large body of evidence that excess returns on stocks and other risky assets are predictable. It is very plausible that risk and risk aversion change over the business cycle, and this is exactly the horizon at which we see predictable excess returns (see e.g. Fama and French (1989)).; Using the S&P 500 index options, we first examine the empirical option pricing performance of the Markov mixture of normals (MMN) approach relative to some benchmark and leading alternative models. Based on the MMN dynamics for the S&P 500 index, we further conduct statistical inference on the options implied risk aversion functions in the context of a representative agent equilibrium model. The proposed Bayesian approach provides intuitive and exact inference for any non-linear function of the parameters instead of relying on asymptotic distributions.