Moments structure of ℓ <Subscript>1</Subscript>-stochastic volatility models

We consider Taylor’s stochastic volatility model (SVM) when the innovations of the hidden log-volatility process have a Laplace distribution (ℓ <Subscript>1</Subscript> exponential density), rather than the standard Gaussian distribution (ℓ <Subscript>2</Subscript>) usually employed. Recently many investigations have employed ℓ <Subscript>1</Subscript> metric to allow better modeling of the abrupt changes of regime observed in financial time series. However, the estimation of SVM is known to be difficult because it is a non-linear with an hidden markov process. Moreover, an additional difficulty yielded by the use of ℓ <Subscript>1</Subscript> metric is the not differentiability of the likelihood function. An alternative consists in using a generalized or efficient method-of-moments (GMM/EMM) estimation. For this purpose, we derive here the moments and autocovariance function of such ℓ <Subscript>1</Subscript>-based stochastic volatility models. Copyright Springer Science+Business Media B.V. 2012