Bayesian Value-at-Risk for a Portfolio: Multi- and Univariate Approaches Using MSF-SBEKK Models

• Authors: Jacek Osiewalski , Anna Pajor
• Languages of publication: EN

Abstracts

EN

The s-period ahead Value-at-Risk (VaR) for a portfolio of dimension n is considered and its Bayesian analysis is discussed. The VaR assessment can be based either on the n-variate predictive distribution of future returns on individual assets, or on the univariate Bayesian model for the portfolio value (or the return on portfolio). In both cases Bayesian VaR takes into account parameter uncertainty and non-linear relationship between ordinary and logarithmic returns. In the case of a large portfolio, the applicability of the n-variate approach to Bayesian VaR depends on the form of the statistical model for asset prices. We use the n-variate type I MSF-SBEKK(1,1) volatility model proposed specially to cope with large n. We compare empirical results obtained using this multivariate approach and the much simpler univariate approach based on modelling volatility of the value of a given portfolio.

Keywords

EN

Bayesian econometrics; risk analysis; multivariate GARCH processes; multivariate SV processes; hybrid SV-GARCH models

• Publisher: Polska Akademia Nauk Oddział w Łodzi
• Journal: Central European Journal of Economic Modelling and Econometrics
• Year: 2010
• Volume: 2
• Issue: 4
• Pages: 253-277

Dates

received

2010-12-07

accepted

2011-03-31

Contributors

author

Jacek Osiewalski

• Cracow University of Economics

author

Anna Pajor

• Cracow University of Economics