Advances in stochastic volatility modeling

Abstract

So et al. (2002) incorporated a fixed threshold value into the autoregressive stochastic volatility model to capture the asymmetric property of both the mean and the volatility in financial time series. In this thesis, we generalize So's model by allowing the threshold value be unknown. The traditional threshold model uses piecewise linear structures to describe nonlinear features in a parsimonious way but suffers the improper regime-switching when observations are close to the threshold value. Thus, we further develop the threshold stochastic volatility autoregressive (TARSV) model to the buffered autoregressive stochastic volatility (BARSV) model using the buffer zone to replace the traditional threshold variable. The buffer zone does not only mitigate the side-effect of the estimation error of the threshold variable but also captures the hysteretic phenomenon in the real case. Due to the latent structure in the stochastic volatility model and the discontinuity of the likelihood caused by the threshold variable, Bayesian method is employed for parameter estimation. Simulation experiments are carried out to verify the validity of the estimation method. Empirical applications are studied using financial time series data. Using BIC and DIC, we compare the validity of the TARSV and BARSV models.