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Working Paper
Bayesian semiparametric multivariate GARCH modeling
This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature, the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and nonconjugate methods, which provide mixing over both the location and scale of the normal components. MCMC methods are ...
Working Paper
Risk, Return, and Volatility Feedback: A Bayesian Nonparametric Analysis
The relationship between risk and return is one of the most studied topics in finance. The majority of the literature is based on a linear, parametric relationship between expected returns and conditional volatility. This paper models the contemporaneous relationship between market excess returns and contemporaneous log-realized variances nonparametrically with an infinite mixture representation of their joint distribution. The conditional distribution of excess returns given log-realized variance will also have an infinite mixture representation but with probabilities and arguments depending ...
Working Paper
Estimating a semiparametric asymmetric stochastic volatility model with a Dirichlet process mixture
In this paper, we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility distribution with an infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t ...
Working Paper
Bayesian semiparametric stochastic volatility modeling
This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, we use nonparametric Bayesian methods to flexibly model the skewness and kurtosis of the distribution while continuing to model the dynamics of volatility with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. We present a Markov chain Monte Carlo sampling approach to estimation with ...