Asymmetric Stochastic Volatility Models: Properties and ABC Filter-based Maximum Likelihood Estimation

In this paper, we derive the statistical properties of a general family of Stochastic Volatility (SV) models with leverage effect which capture the dynamic evolution of asymmetric volatility in financial returns. We provide analytical expressions of moments and autocorrelations of power-transformed absolute returns. Moreover, we analyze and compare the finite sample performance of two estimation procedures. The first method is an Approximate Bayesian Computation (ABC) filter-based Maximum Likelihood (ML), a technique similar to indirect inference as it requires simulation of pseudo-observations which are weighted according to their distance to the true observations. The second estimation method is a Markov Chain Monte Carlo (MCMC) estimator implemented in BUGS, a user-friendly and freely available software package that automatically calculates the full conditional posterior distribution. We show that the ABC filter-based ML estimator has better finite sample properties when estimating the parameters of a very general specification of the log-volatility with standardized returns following the Generalized Error Distribution (GED). The results are illustrated by analyzing a series of daily S&P500 returns.