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Moments structure of ℓ 1-stochastic volatility models

Neto, David ; Sardy, Sylvain

In: Quality & Quantity, 2012, vol. 46, no. 6, p. 1947-1952

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    Title
    • Moments structure of ℓ 1-stochastic volatility models
    Author
    • Neto, David. Department of Econometrics, University of Geneva, 1211, Geneva 4, Switzerland
    • Sardy, Sylvain. Department of Mathematics, University of Geneva, 1211, Geneva 4, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:320806
    Summary
    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