Asymmetric stochastic volatility models: properties and particle filter-based simulated maximum likelihood estimation

Abstract

The statistical properties of a general family of asymmetric stochastic volatility (A-SV)models which capture the leverage effect in financial returns are derived providing analyt- ical expressions of moments and autocorrelations of power-transformed absolute returns.The parameters of the A-SV model are estimated by a particle filter-based simulated max- imum likelihood estimator and Monte Carlo simulations are carried out to validate it. Itis shown empirically that standard SV models may significantly underestimate the value- at-risk of weekly S&P 500 returns at dates following negative returns and overestimate itafter positive returns. By contrast, the general specification proposed provide reliable fore- casts at all dates. Furthermore, based on daily S&P 500 returns, it is shown that the mostadequate specification of the asymmetry can change over time.