2012 | 895 | 5-18
Article title

Modele hybrydowe MSV-MGARCH z dwoma procesami ukrytymi

Title variants
Hybrid MSV-MGARCH Models with Two Latent Processes
Languages of publication
In order to efficiently model the price volatility of a large number of financial assets, Osiewalski and Pajor (2007, 2009) and Osiewalski (2009) introduced multivariate hybrid MSV–MGARCH models. Their conditional covariance matrix is a product of a univariate latent process and a matrix with a simple MGARCH structure (Engle’s DCC, scalar BEKK). The proposed hybrid models are useful thanks to their good fit and ability to jointly handle as many as 50 assets. However, one latent process may be insufficient in the case of a heterogenous portfolio. In this study we propose a more general hybrid structure that uses two latent processes. We present full Bayesian inference for the model and suggest an MCMC strategy for simulations from the posterior distribution. Two formal Bayesian model comparisons are given. They show the advantages of using two latent processes. In particular, our approach is applied to jointly model the volatility of four time series: two stock indices and the prices of gold and silver. We formally compare the joint model and two separate models (for indices and for metal prices).
  • Uniwersytet Ekonomiczny w Krakowie, Katedra Ekonometrii i Badań Operacyjnych, ul. Rakowicka 27, 31-510 Kraków, Poland,
  • Bauwens L., Laurent S., Rombouts J.V.K. [2006], Multivariate GARCH Models: A Survey, „Journal of Applied Econometrics” 21.
  • Osiewalski J. [2009], New Hybrid Models of Multivariate Volatility (a Bayesian Perspective), „Przegląd Statystyczny (Statistical Review)” 56.
  • Osiewalski J., Pajor A. [2007], Flexibility and Parsimony in Multivariate Financial Modelling: A Hybrid Bivariate DCC–SV Model [w:] Financial Markets. Principles of Modeling, Forecasting and Decision-Making, FindEcon Monograph Series No. 3, eds W. Milo, P. Wdowiński, Łódź University Press, Łódź.
  • Osiewalski J., Pajor A. [2009], Bayesian Analysis for Hybrid MSF–SBEKK Models of Multivariate Volatility, „Central European Journal of Economic Modelling and Econometrics” 1.
  • Osiewalski J., Pajor A. [2010], Bayesian Value-at-Risk for a Portfolio: Multi- and Univariate Approaches Using MSF-SBEKK Models, „Central European Journal of Economic Modelling and Econometrics” 2.
  • Osiewalski J., Pajor A. [2012], Bayesian Value-at-Risk and Expected Shortfall for a Large Portfolio (Multi- and Univariate Approaches), „Acta Physica Polonica A”.
  • Osiewalski J., Pajor A., Pipień M. [2007], Bayesian Comparison of Bivariate GARCH, SV and Hybrid Models [w:] MACROMODELS’2006, Proceedings of the 33rd International Conference, eds W. Welfe, A. Welfe, Absolwent, Łódź.
  • Pajor A. [2010], Wielowymiarowe procesy wariancji stochastycznej w ekonometrii finansowej – ujęcie bayesowskie, Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie, Kraków.
Document Type
Publication order reference
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