A Generalized Dynamic Conditional Correlation Model for Portfolio Risk Evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle [R.F. Engle, Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics 20 (2002) 339-350] and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al.[L. Cappiello, R.F. Engle, K. Sheppard, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 25 (2006) 537-572]. The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. [M. Billio, M. Caporin, M. Gobbo, Flexible dynamic conditional correlation multivariate GARCH for asset allocation, Applied Financial Economics Letters 2 (2006) 123-130] and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation.

[1]  Massimiliano Caporin,et al.  Evaluating Value-at-Risk Measures in Presence of Long Memory Conditional Volatility , 2008 .

[2]  Paul H. Kupiec,et al.  Techniques for Verifying the Accuracy of Risk Measurement Models , 1995 .

[3]  R. Engle,et al.  Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns , 2003, SSRN Electronic Journal.

[4]  M. McAleer.  Automated Inference and Learning in Modelling Financial Volatility * , 2004 .

[5]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[6]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[7]  Michael McAleer,et al.  ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL , 2003, Econometric Theory.

[8]  Y. Tse,et al.  A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model With Time-Varying Correlations , 2002 .

[9]  P. Franses,et al.  A Generalized Dynamic Conditional Correlation Model for Many Asset Returns , 2003 .

[10]  R. Engle,et al.  Multivariate Simultaneous Generalized ARCH , 1995, Econometric Theory.

[11]  M. McAleer,et al.  Dynamic Asymmetric GARCH , 2006 .

[12]  L. Bauwens,et al.  Multivariate GARCH Models: A Survey , 2003 .

[13]  Zhuanxin Ding,et al.  Large Scale Conditional Covariance Matrix Modeling, Estimation and Testing , 2001 .

[14]  Michael McAleer,et al.  GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION , 2008, Econometric Theory.

[15]  Jose A. Lopez,et al.  Methods for Evaluating Value-at-Risk Estimates , 1998 .

[16]  T. Bollerslev,et al.  Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model , 1990 .

[17]  M. McAleer,et al.  Multivariate Stochastic Volatility: A Review , 2006 .

[18]  Offer Lieberman,et al.  Asymptotic theory for multivariate GARCH processes , 2003 .

[19]  Monica Billio,et al.  Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation , 2006 .