Bayesian Analysis of Stock Index Return Volatility

The stochastic volatility is a universal phenomenon in financial time series, and an important issue in risk management research. In this paper, through the statistical structure of the standard stochastic volatility model, we infer the SV model´s likelihood function, design the parameters´ conjugate prior distribution, obtain the corresponding model parameter according to the Bayesian theorem, and examine their condition distribution. Furthermore, in order to obtain the model parameter estimation and their confidence intervals, we use Gibbs sampling to devise an MCMC computational procedure, and carry out an empirical analysis using the Shanghai composite index and the Shenzhen component index data. The results indicate that the Bayesian method is an effective tool to explore the financial time series data.