Building statistical model for financial asset returns: New stochastic volatility model

Real stock market data show that the daily stock log-returns are locally stationary but not in a long period. Various stochastic volatility models for these data have been proposed in the literature. Since more data become available, it is helpful to take a closer look at financial data from a statistical point of view. Our exploratory analysis leads to two new stochastic volatility models with the inverse of volatility being modeled by a Gamma moving average or autoregressive process. We develop Markov chain Monte Carlo (MCMC) algorithms for Bayesian estimation of these models. The models are extensively checked and compared with the popular GARCH model in terms of volatility and prediction distribution. We find that estimated volatility and prediction distribution from the new models are markedly better than those produced by the GARCH model.