Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets

The market microstructure (MM) models using normal distribution are useful tools for modeling financial time series, but they cannot explain essential characteristics of skewness and heavy tails, which may occur in a market. To cope with this problem, a heavy-tailed market microstructure model based on Student-tt distribution (MM-tt) is proposed in this paper. Under the assumption of non-normality, an efficient Markov chain Monte Carlo (MCMC) method is developed for parameter estimation of the proposed model. The simulation study verifies the effectiveness of the estimation approach. In empirical study, the proposed model for various stock market indices is compared to the MM models with other distributions, such as the normal distribution and a mixture of two normal distributions. Empirical results indicate that the stock prices/returns have heavy tails and the MM-tt model provides a better fit than the MM models with other distributions for some financial time series. Comparison of some different type models is also done, which demonstrates that the MM-tt model fits the three indices better than the stochastic volatility (SV-tt) model with Student-tt distribution.