Stochastic Volatility: Univariate and Multivariate Extensions
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(2) CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisationsmembres, d=une subvention d=infrastructure du ministère de l=Industrie, du Commerce, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Québec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the Ministère de l=Industrie, du Commerce, de la Science et de la Technologie, and grants and research mandates obtained by its research teams. Les organisations-partenaires / The Partner Organizations $École des Hautes Études Commerciales $École Polytechnique $Université Concordia $Université de Montréal $Université du Québec à Montréal $Université Laval $Université McGill $MEQ $MICST $Alcan Aluminium Ltée $Banque Nationale du Canada $Bell Québec $Développement des ressources humaines Canada (DRHC) $Egis $Fédération des caisses populaires Desjardins de Montréal et de l=Ouest-du-Québec $Hydro-Québec $Imasco $Industrie Canada $Microcell Labs inc. $Raymond Chabot Grant Thornton $Téléglobe Canada $Ville de Montréal © 1999 Éric Jacquier, Nicholas G. Polson et Peter E. Rossi. Tous droits réservés. All rights reserved. Reproduction partielle permise avec citation du document source, incluant la notice ©. Short sections may be quoted without explicit permission, provided that full credit, including © notice, is given to the source. Ce document est publié dans l=intention de rendre accessibles les résultats préliminaires de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions. Les idées et les opinions émises sont sous l=unique responsabilité des auteurs, et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents preliminary research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners. ISSN 1198-8177.
(3) Stochastic Volatility: Univariate and Multivariate Extensions* Éric JacquierH, Nicholas G. PolsonI, Peter E. Rossi' Résumé / Abstract Les modèles de volatilité stochastique, alias SVOL, sont plus durs à estimer que les modèles traditionnels de type ARCH. La littérature récente offre des estimateurs éprouvés pour un modèle SVOL univarié de base. Ce modèle est trop contraignant pour une utilisation en économie financière. Les prévisions de volatilité qu'il produit peuvent etre biaisées, particulièrement quand la volatilité est élevée. Nous généralisons le modèle de base en y ajoutant des effets de levier par le biais d'une corrélation entre les chocs observables et de variance, et la possibilité de distributions conditionnelles à queues épaisses. Nous développons un algorithme bayésien à chaînes markoviennes de Monte Carlo. Nous développons aussi un algorithme pour l'analyse d'un modèle SVOL multivarié à facteurs. Ces estimateurs permettent une inférence en échantillon fini pour les paramètres et les volatilités. Nous documentons les performances de l'estimateur et montrons que les extensions sont nécessaires. Nous testons la normalité des distributions conditionnelles. Cette méthode est mise en œuvre sur plusieurs séries financières. Il y a une forte évidence (1) de distributions conditionnelles à queues épaisses, et (2) d'effets de levier pour les actifs financiers. Les résultats sont robustes et ont d'importantes implications sur les décisions fondées sur les prédictions de volatilité, particulièrement pour la gestion de risques. Stochastic volatility models, aka SVOL, are more difficult to estimate than standard time-varying volatility models (ARCH). Advances in the literature now offer well tested estimators for a basic univariate SVOL model. However, the basic model is too restrictive for many economic and finance applications. The use of the basic model can lead to biased volatility forecasts especially around crucial periods of high volatility. We extend the basic SVOL needs to allow for the *. Corresponding Author: Éric Jacquier, Finance Department, Fulton Hall 224B, Boston College, Chestnut Hill, MA 02167, USA Tel: (617) 552-2943 Fax: (617) 552-0431 email: jacquier@jacquier.bd.edu Essential support from the Institute for Quantitative Research in Finance (Q GROUP) and CIRANO is gratefully acknowledged. We also thank the Physics Department at Boston College for their hospitality on the Theoretical Physics Computing Facility. We received helpful comments from Torben Andersen, Tim Bollerslev, John Geweke, Eric Ghysels, Dan Nelson, Éric Renault, Esther Ruiz, George Tauchen, Harald Uhlig, the participants of the Econometrics seminar at Harvard, and the 1994 CIRANO conference on stochastic volatility. We are especially grateful for detailed comments from two anonymous referees and the associate editor.. †. Boston College and CIRANO. ‡. University of Chicago. §. University of Chicago.
(4) leverage effect, through a correlation between observable and variance errors, and fat-tails in the conditional distribution. We develop a Bayesian Markov Chain Monte Carlo algorithm for this extended model. We also provide an algorithm to analyze a multivariate factor SVOL model. The method simultaneously performs finite sample inference and smoothing. We document the performance of the estimator and show why the extensions are warranted. We provide the researcher with a range of model diagnostics, such as the identification of outliers for stochastic volatility models or the assessment of the normality of the conditional distribution. We implement this methodology on a number of univariate financial time series. There is strong evidence of (1) non-normal conditional distributions for most series, and (2) a leverage effect for stock returns. We illustrate the robustness of the results to the choice of the prior distributions. These results have policy implications on decisions based upon prediction of volatility, especially when dealing with tail prediction as in risk management.. Mots Clés :. Volatilité stochastique, ARCH, algorithme MCMC, effets de levier, gestion de risque, distributions à queues épaisses. Keywords:. Stochastic volatility, ARCH, MCMC algorithm, leverage effect, risk management, fat-tailed distributions. JEL: C1, C11, C15, G1.
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+7
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