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On leverage in a stochastic volatility model. (English) Zbl 1335.91116
Summary: This paper is concerned with the specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications co-exist in the literature. One is the Euler approximation to the well-known continuous time SV model with leverage effect and the other is the discrete time SV model of E. Jacquier et al. [J. Econom. 122, No. 1, 185–212 (2004; Zbl 1328.91254)]. Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain and interpret the leverage effect in the model of Jacquier et al. Empirical comparisons of these two models via Bayesian Markov chain Monte Carlo (MCMC) methods further reveal that the specification of Jacquier et al. is inferior. Simulation experiments are conducted to study the sampling properties of Bayes MCMC for the conventional model.

MSC:
91G70 Statistical methods; risk measures
91B70 Stochastic models in economics
Software:
BUGS
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