Asymmetric Stochastic Volatility Models: Properties and 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 the finite sample performance of an Approximate Bayesian Computation (ABC) filter-based Maximum Likelihood (ML) estimator, a technique similar to indirect inference as it requires simulation of pseudo-observations which are weighted according to their distance to the true observations. We show that the ABC filter-based ML estimator does a remarkably good job in 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.