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Moments structure of ℓ 1 -stochastic volatility models


  • David Neto


  • Sylvain Sardy



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

Suggested Citation

  • David Neto & Sylvain Sardy, 2012. "Moments structure of ℓ 1 -stochastic volatility models," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(6), pages 1947-1952, October.
  • Handle: RePEc:spr:qualqt:v:46:y:2012:i:6:p:1947-1952
    DOI: 10.1007/s11135-011-9459-4

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    References listed on IDEAS

    1. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    2. Sardy, Sylvain & Tseng, Paul, 2004. "On the Statistical Analysis of Smoothing by Maximizing Dirty Markov Random Field Posterior Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 191-204, January.
    3. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
    4. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
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    More about this item


    Stochastic volatility model; Laplace innovations; Autocovariance function; Variance gamma model; C22;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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