One for all : nesting asymmetric stochastic volatility models

This paper proposes a new stochastic volatility model to represent the dynamic evolution of conditionally heteroscedastic time series with leverage effect. Although there are already several models proposed in the literature with the same purpose, our main justification for a further new model is that it nests some of the most popular stochastic volatility specifications usually implemented to real time series of financial returns. We derive closed-form expressions of its statistical properties and, consequently, of those of the nested specifications. Some of these properties were previously unknown in the literature although the restricted models are often fitted by empirical researchers. By comparing the properties of the restricted models, we are able to establish the advantages and limitations of each of them. Finally, we analyze the performance of a MCMC estimator of the parameters and volatilities of the new proposed model and show that, if the error distribution is known, it has appropriate finite sample properties. Furthermore, estimating the new model using the MCMC estimator, one can correctly identify the restricted true specifications. All the results are illustrated by estimating the parameters and volatilities of simulated time series and of a series of daily S&P500 returns