Stochastic volatility model under a discrete mixture-of-normal specification

This paper investigates the properties of a linearized stochastic volatility (SV) model originally from Harvey et al. (Rev Econ Stud 61:247–264, 1994) under an extended flexible specification (discrete mixtures of normal). General closed form expressions for the moment conditions are derived. We show that our proposed model captures various tail behavior in a more flexible way than the Gaussian SV model, and it can accommodate certain correlation structure between the two innovations. Rather than using likelihood-based estimation methods via MCMC, we use an alternative procedure based on the characteristic function (CF). We derive analytical expressions for the joint CF and present our estimator as the minimizer of the weighted integrated mean-squared distance between the joint CF and its empirical counterpart (ECF). We complete the paper with an empirical application of our model to three stock indices, including S&P 500, Dow Jones 30 Industrial Average index and Nasdaq Composite index. The proposed model captures the dynamics of the absolute returns well and presents some consistent and supportive evidence for the Taylor effect and Machina effect.