Moments structure of ℓ 1 -stochastic volatility models

David Neto and Sylvain Sardy ()

Quality & Quantity: International Journal of Methodology, 2012, vol. 46, issue 6, 1947-1952

Abstract: We consider Taylor’s stochastic volatility model (SVM) when the innovations of the hidden log-volatility process have a Laplace distribution (ℓ 1 exponential density), rather than the standard Gaussian distribution (ℓ 2 ) usually employed. Recently many investigations have employed ℓ 1 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 1 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 1 -based stochastic volatility models. Copyright Springer Science+Business Media B.V. 2012

Keywords: Stochastic volatility model; Laplace innovations; Autocovariance function; Variance gamma model; C22 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11135-011-9459-4

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