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Models and Priors for Multivariate Stochastic Volatility

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  • Éric Jacquier

    ()

  • Nicholas G. Polson
  • Peter E. Rossi

Abstract

Discrete time stochastic volatility models (hereafter SVOL) are noticeably harder to estimate than the successful ARCH family of models. In this paper, we develop methods for finite sample inference, smoothing, and prediction for a number of univariate and multivariate SVOL models. Specifically, we model fat-tailed and skewed conditional distributions, correlated errors distributions (leverage effect), and two multivariate models, a stochastic factor structure model and a stochastic discount dynamic model. We specify the models as a hierarchy of conditional probability distributions: p(data/volatilities), p(volatilities/ parameters) and p(parameters). This hierarchy provides a natural environment for the construction of stochastic volatility models that depart from standard distributional assumptions. Given a model and the data, inference and prediction are based on the joint posterior distribution of the volatilities and the parameters which we simulate via Markov chain Monte Carlo (MCMC) methods. Our approach also provides a sensitivity analysis for parameter inference and an outlier diagnostic. Our framework, therefore, provides a general perspective on specification and implementation of stochastic volatility models. We apply various extensions of the basic SVOL model to many financial time series. We find strong evidence of non-normal conditional distributions for stock returns and exchange rates. We also find some evidence of correlated errors for stock returns. These departures from the basic model affect persistence and therefore should be incorporated if the model is used for variance prediction. Les modèles de volatilité stochastique (ci-après) SVOL sont singulièrement plus difficiles à estimer que les modèles de type ARCH qui connaissent un grand succès. Dans cet article, nous développons des méthodes en échantillons finis pour l'inférence et la prédiction, ceci pour un nombre de modèles SVOL univariés et multivariés. Plus précisément nous modélisons des distributions conditionnelles non-normales, des modèles avec effets de levier, et deux modèles multivariés; un modèle a structure de facteurs et un modèle d'escompte dynamique. Nous spécifions les modèles par une hiérarchie de distributions conditionnelles : p(données|volatilités), p(volatilités|paramètres), et p(paramètres). Cette hiérarchie fournit un environnement naturel pour l'élaboration de modèles de volatilité stochastique plus généraux que le modèle de base. Pour un modèle et un échantillon, l'inférence et la prédiction sont fondées sur la distribution postérieure jointe des volatilités et des paramètres que nous simulons avec des méthodes de Chaînes de Markov et de Monte Carlo (MCMC). Notre approche fournit aussi une analyse de sensitivité pour les paramètres et une analyse pour les outliers. Le cadre d'estimation fournit donc une perspective générale sur la spécification et l'implémentation des modèles de volatilité stochastique. Nous appliquons plusieurs extensions du modèle SVOL de base à de nombreuses séries financières. Il y a une forte évidence de non-normalité des distributions conditionnelles. Il y aussi une certaine évidence de corrélation des erreurs pour les retours sur actions. Ces élaborations du modèle de base ont une influence sur la persistance et devraient être incorporées en vue de prédictions de volatilité.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 95s-18.

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Date of creation: 01 Mar 1995
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Handle: RePEc:cir:cirwor:95s-18

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Related research

Keywords: Stochastic volatility; Forecasting and smoothing; Metropolis algorithm; Volatilité stochastique ; Inférence et prédiction ; Algorythme Metropolis;

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References

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  1. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  2. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Ronald Mahieu & Peter Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis.
  4. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  5. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  6. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  7. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  8. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  9. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
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Cited by:
  1. Nunzio Cappuccio & Diego Lubian & Davide Raggi, 2003. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatily Model," Working Papers 7, University of Verona, Department of Economics.
  2. Manabu Asai & Massimiliano Caporin & Michael McAleer, 2010. "Block Structure Multivariate Stochastic Volatility Models," Working Papers in Economics 10/24, University of Canterbury, Department of Economics and Finance.
  3. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo.
  4. Charles S. Bos, 2008. "Model-based Estimation of High Frequency Jump Diffusions with Microstructure Noise and Stochastic Volatility," Tinbergen Institute Discussion Papers 08-011/4, Tinbergen Institute.
  5. repec:dgr:uvatin:2008011 is not listed on IDEAS

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