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Indirect estimation of alpha-stable stochastic volatility models

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Abstract

The alpha-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its many useful properties, including a central limit theorem, are especially appreciated in the financial field. However, estimation difficulties have up to now hindered its diffusion among practitioners. In this paper we propose an indirect estimation approach to stochastic volatility models with alpha-stable innovations that exploits, as auxiliary model, a GARCH(1,1) with t-distributed innovations. We consider both cases of heavytailed noise in the returns or in the volatility. The approach is illustrated by means of a detailed simulation study and an application to currency crises.

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  • Marco Lombardi & Giorgio Calzolari, 2006. "Indirect estimation of alpha-stable stochastic volatility models," Econometrics Working Papers Archive wp2006_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  • Handle: RePEc:fir:econom:wp2006_07
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    Cited by:

    1. Anna Gottard & Giorgio Calzolari, 2014. "Alternative estimating procedures for multiple membership logit models with mixed effects: indirect inference and data cloning," Econometrics Working Papers Archive 2014_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    2. Matteo Barigozzi & Roxana Halbleib & David Veredas, "undated". "Which model to match?," ULB Institutional Repository 2013/136240, ULB -- Universite Libre de Bruxelles.
    3. Giorgio Calzolari & Roxana Halbleib, 2014. "Estimating Stable Factor Models By Indirect Inference," Working Paper Series of the Department of Economics, University of Konstanz 2014-25, Department of Economics, University of Konstanz.
    4. Johan Dahlin & Mattias Villani & Thomas B. Schon, 2015. "Bayesian optimisation for fast approximate inference in state-space models with intractable likelihoods," Papers 1506.06975, arXiv.org, revised Jun 2017.
    5. Calzolari, Giorgio & Halbleib, Roxana & Parrini, Alessandro, 2014. "Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 158-171.
    6. Parrini, Alessandro, 2012. "Indirect estimation of GARCH models with alpha-stable innovations," MPRA Paper 38544, University Library of Munich, Germany.
    7. Dasheng Ji & B. Brorsen, 2011. "A recombining lattice option pricing model that relaxes the assumption of lognormality," Review of Derivatives Research, Springer, vol. 14(3), pages 349-367, October.
    8. Giorgio Calzolari & Roxana Halbleib & Alessandro Parrini, 2012. "Indirect Estimation of α-Stable Garch Models," Working Paper Series of the Department of Economics, University of Konstanz 2012-31, Department of Economics, University of Konstanz.

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