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Forecasting Value-at-Risk Using Block Structure Multivariate Stochastic Volatility Models

Asai, Manabu and Caporin, Massimiliano and McAleer, Michael (2012) Forecasting Value-at-Risk Using Block Structure Multivariate Stochastic Volatility Models. [Working Paper or Technical Report] (Submitted)

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Abstract

Most multivariate variance or volatility models suffer from a common problem, the “curse of dimensionality”. For this reason, most are fitted under strong parametric restrictions that reduce the interpretation and flexibility of the models. Recently, the literature has focused on multivariate models with milder restrictions, whose purpose was to combine the need for interpretability and efficiency faced by model users with the computational problems that may emerge when the number of assets is quite large. We contribute to this strand of the literature proposing a block-type parameterization for multivariate stochastic volatility models. The empirical analysis on stock returns on US market shows that 1% and 5 % Value-at-Risk thresholds based on one-step-ahead forecasts of covariances by the new specification are satisfactory for the period includes the global financial crisis.

Item Type:Working Paper or Technical Report
Additional Information:JEL classifications: C32, C51, C10.
Uncontrolled Keywords:Block structures, Multivariate stochastic volatility, Curse of dimensionality, Leverage effects; Multi-factors, Heavy-tailed distribution.
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
Volume:2012
Number:3
ID Code:14621
References:

Ait-Sahalia, Y., and M.W. Brandt (2001), “Variable Selection for Portfolio Choice”, Journal of Finance, 56, 1297-1351.

Aguilar, O. and M. West (2000), “Bayesian Dynamic Factor Models and Portfolio Allocation”, Journal of Business and Economic Statistics, 18, 338–357.

Alizadeh, S., M. Brandt, and F. Diebold (2002), “Range-Based Estimation of Stochastic Volatility Models”, Journal of Finance, 57, 1047-1091.

Andersen, T.G. (1994), “Stochastic Autoregressive Volatility: A Framework for Volatility Modeling”, Mathematical Finance, 4, 75-102.

Asai, M. (2008), “Autoregressive Stochastic Volatility Models with Heavy-Tailed Distributions: A Comparison with Multifactor Volatility Models”, Journal of Empirical Finance, 15, 332-341.

Asai, M. (2009), “Bayesian Analysis of Stochastic Volatility Models with Mixture-of-Normal Distributions”, Mathematics and Computers in Simulation, 79, 2579-2596.

Asai, M. and M. McAleer (2006), “Asymmetric Multivariate Stochastic Volatility”, Econometric Reviews, 25, 453-473.

Asai, M. and M. McAleer (2009a), “Multivariate Stochastic Volatility, Leverage and News Impact Surfaces”, Econometrics Journal, 12, 292-309.

Asai, M. and M. McAleer (2009b), “The Structure of Dynamic Correlations in Multivariate Stochastic Volatility Models”, Journal of Econometrics, 150, 182-192.

Asai, M., M. McAleer and J. Yu (2006), “Multivariate Stochastic Volatility: A Review”, Econometric Reviews, 25, 145-175.

Billio, M., M. Caporin and M. Gobbo, (2006), “Flexible Dynamic Conditional Correlation Multivariate GARCH for Asset Allocation”, Applied Financial Economics Letters, 2, 123-130.

Bauwens, L., S. Laurent and J.V.K. Rombouts (2006), “Multivariate GARCH: A Survey”, Journal of Applied Econometrics, 21, 79-109.

Bollerslev, T. (1990), “Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Approach”, Review of Economics and Statistics, 72, 498-505.

Bollerslev, T., R.F. Engle and J. Woodridge (1988), “A Capital Asset Pricing Model with Time Varying Covariances”, Journal of Political Economy, 96, 116-131.

Calvet, L.E., A.J. Fisher, and S.B. Thompson (2006), “Volatility Comovement: A Multifrequency Approach”, Journal of Econometrics, 131, 179–215.

Candelon, B., G. Colletaz, C. Hurlin, and S. Tokpavi (2010), “Backtesting Value-at-Risk: A GMM Duration-Based Approach”, to appear in Journal of Financial Econometrics.

Chan, D., R. Kohn, and C. Kirby (2006), “Multivariate Stochastic Volatility Models with Correlated Errors”, Econometric Reviews, 25, 245–274.

Chernov, M., A.R. Gallant, E. Ghysels and G. Tauchen (2003), “Alternative Models for Stock Price Dynamics”, Journal of Econometrics, 116, 225-257.

Chib, S., F. Nardari, and N. Shephard (2002), “Markov Chain Monte Carlo Methods for Generalized Stochastic Volatility Models”, Journal of Econometrics, 108, 281–316.

Chib, S., F. Nardari, and N. Shephard (2006), “Analysis of High Dimensional Multivariate Stochastic Volatility Models”, Journal of Econometrics, 134, 341–371.

Chib, S., Y. Omori and M. Asai (2009), “Multivariate Stochastic Volatility”, in: T.G. Andersen, R.A. Davis, J.-P. Kreiss and T. Mikosch (eds.), Handbook of Financial Time Series, Springer-Verlag, New York, 365-400.

Christoffersen, P. (1998), “Evaluating Interval Forecasts,” International Economic Review, 39, 841–62.

Christoffersen, P., Jacobs, K. and Y. Wang (2008), “Option Valuation with Long-run and Shortrun Volatility Components”, Journal of Financial Economics, 90, 272-297.

Christoffersen, P. and D. Pelletier (2004), “Backtesting Value-at-Risk: A Duration-Based Approach”, Journal of Financial Econometrics, 2, 84-108.

Danielsson, J. (1998), “Multivariate Stochastic Volatility Models: Estimation and a Comparison with VGARCH Models”, Journal of Empirical Finance, 5, 155–173.

Ding, Z. and R.F. Engle (2001), “Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing”, Academia Economic Papers, 1, 83-106.

Elandt, R.C. (1961), “The Folded Normal Distribution: Two Methods of Estimating Parameters from Moments”, Technometrics, 3, 551–562.

Engle, R.F. (2002), “Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models”, Journal of Business and Economic Statistics, 20, 339-350.

Engle, R.F. and K.F. Kroner (1995), “Multivariate Simultaneous Generalized ARCH”, Econometric Theory, 11, 122-150.

Engle, R.F. and G.G.J. Lee (1993), “A Permanent and Transitory Component Model of Stock Return Volatility”, Discussion Paper 92-44R, University of California, San Diego.

Fleming, J., C. Kirby and B. Ostdiek (2001), “The Economic Value of Volatility Timing”, Journal of Finance, 56, 329-352.

Harvey, A.C., E. Ruiz and N. Shephard (1994), “Multivariate Stochastic Variance Models”, Review of Economic Studies, 61, 247-264.

Harvey, A.C. and N. Shephard (1996), “Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns”, Journal of Business and Economic Statistics, 14, 429-434.

Hull, J. and A. White (1987), “The Pricing of Options on Assets with Stochastic Volatility”, Journal of Finance, 42, 281-300.

Koopman, S.J. and E.H. Uspensky (2002), “The Stochastic Volatility in Mean Model: Empirical Evidence from International Stock Markets”, Journal of Applied Econometrics, 17, 667-689.

Lehar, A., M. Scheicher and C. Schittenkopf (2002), “GARCH vs. Stochastic Volatility: Option Pricing and Risk Management”, Journal of Banking and Finance, 23, 323-345.

Leone, F.C., L.S. Nelson, and R.B. Nottingham (1961), “The Folded Normal Distribution”, Technometrics, 3, 543–550.

Liesenfeld, R. and R.C. Jung (2000), “Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions,” Journal of Applied Econometrics, 15, 137-160.

Lopes, H.F. and C.M. Carvalho (2007), “Factor stochastic volatility with time varying loadings and Markov switching regimes”, Journal of Statistical Planning and Inference, 137, 3082 – 3091.

McAleer, M. (2005), “Automated Inference and Learning in Modeling Financial Volatility”, Econometric Theory, 21, 232-261.

Pitt, M.K. and N. Shephard (1999), “Time Varying Covariances: A Factor Stochastic Volatility Approach”, in J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith (Eds.), Bayesian Statistics, Volume 6, Oxford University Press, 547–570.

Shephard, N. (1996), “Statistical Aspects of ARCH and Stochastic Volatility”, in: D. R. Cox, D. V. Hinkley, and O. E. Barndorff-Nielsen (Eds.), Time Series Models in Econometrics, Finance and Other Fields, Chapman & Hall, London, 1-67.

Taylor, S.J. (1986), Modelling Financial Time Series, Chichester, Wiley.

Tse, Y.K. and A.K.C. Tsui, (2002), “A Multivariate GARCH Model with Time-Varying Correlations”, Journal of Business and Economic Statistics, 20, 351-362.

Yu, J. and R. Meyer (2006), “Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison”, Econometric Reviews, 25, 361–384.

Deposited On:05 Mar 2012 12:27
Last Modified:06 Feb 2014 10:05

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