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

Author

Listed:
  • Jacek Osiewalski

    (Cracow University of Economics)

  • Anna Pajor

    (Cracow University of Economics)

Abstract
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.

Suggested Citation

  • Jacek Osiewalski & Anna Pajor, 2010. "Bayesian Value-at-Risk for a Portfolio: Multi- and Univariate Approaches Using MSF-SBEKK Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 2(4), pages 253-277, September.
    • Handle: RePEc:psc:journl:v:2:y:2010:i:4:p:253-277
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    References listed on IDEAS

    as
    1. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 1(2), pages 179-202, November.
    2. Susan Thomas & Mandira Sarma & Ajay Shah, 2003. "Selection of Value-at-Risk models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(4), pages 337-358.
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    Citations

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    Cited by:

    1. Piotr Fiszeder, 2011. "Minimum Variance Portfolio Selection for Large Number of Stocks – Application of Time-Varying Covariance Matrices," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 11, pages 87-98.
    2. Jacek Osiewalski & Krzysztof Osiewalski, 2016. "Hybrid MSV-MGARCH Models – General Remarks and the GMSF-SBEKK Specification," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 8(4), pages 241-271, December.
    3. Pajor Anna & Wróblewska Justyna, 2017. "VEC-MSF models in Bayesian analysis of short- and long-run relationships," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-22, June.
    4. Bassetti, Federico & De Giuli, Maria Elena & Nicolino, Enrica & Tarantola, Claudia, 2018. "Multivariate dependence analysis via tree copula models: An application to one-year forward energy contracts," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1107-1121.
    5. Ewa Ratuszny, 2013. "Robust Estimation in VaR Modelling - Univariate Approaches using Bounded Innovation Propagation and Regression Quantiles Methodology," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 5(1), pages 35-63, March.
    6. Mateusz Pipień, 2013. "Orthogonal Transformation of Coordinates in Copula M-GARCH Models – Bayesian analysis for WIG20 spot and futures returns," NBP Working Papers 151, Narodowy Bank Polski.
    7. Anna Pajor & Justyna Wróblewska & Łukasz Kwiatkowski & Jacek Osiewalski, 2024. "Hybrid SV‐GARCH, t‐GARCH and Markov‐switching covariance structures in VEC models—Which is better from a predictive perspective?," International Statistical Review, International Statistical Institute, vol. 92(1), pages 62-86, April.

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    More about this item

    Keywords

    Bayesian econometrics; risk analysis; multivariate GARCH processes; multivariate SV processes; hybrid SV-GARCH models;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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