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

• Autorzy: Jacek Osiewalski , Anna Pajor
• Języki publikacji: EN

Abstrakty

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. (original abstract)

Słowa kluczowe

PL

Ekonometria bayesowska; Analiza ryzyka; Model GARCH; Procesy zmienności stochastycznej

EN

Bayesian econometric; Risk analysis; GARCH model; Stochastic Volatility Processes

• Czasopismo: Central European Journal of Economic Modelling and Econometrics (CEJEME)
• Rocznik: 2010
• Tom: 2
• Numer: nr 4
• Strony: 253-277

Twórcy

autor

Jacek Osiewalski

• Cracow University of Economics, Poland

autor

Anna Pajor

• Cracow University of Economics, Poland

Bibliografia

• [1] Artzner P., Delbaen F., Eber J.-M., Heath D., (1999), Coherent measures of risk, "Mathematical Finance" 9, 203-228.
• [2] Bauwens L., Laurent S., Rombouts J.V.K., (2006), Multivariate GARCH models: A survey, "Journal of Applied Econometrics" 21, 79-109.
• [3] Engle R., Manganelli S., (2004), CAViaR: conditional autoregressive Value at Risk by regression quantiles, "Journal of Business and Economic Statistics" 22, 367-381.
• [4] Lee T. H., (2008), Loss Functions in Time Series Forecasting, [in:] International Encyclopedia of the Social Sciences, 2nd edition. Vol. 4, Macmillan Reference USA, Detroit.
• [5] Lopez J.A., (1998), Testing your risk tests, The Financial Survey, May-June, 18-20.
• [6] O'Hagan A., (1994), Bayesian Inference, Edward Arnold, London.
• [7] Osiewalski J., (2009), New hybrid models of multivariate volatility (a Bayesian perspective), "Przegląd Statystyczny" (Statistical Review) 56, 15-22.
• [8] Osiewalski J., Pajor A., (2009), Bayesian analysis for hybrid MSF-SBEKK models of multivariate volatility, "Central European Journal of Economic Modelling and Econometrics" 1, 179-202.
• [9] Pajor A., (2005), Bayesian comparison of bivariate SV models for two related time series, "Acta Universitatis Lodziensis - Folia Oeconomica" 190, 177-196.
• [10] Sarma M., Thomas S., Shah A., (2003), Selection of Value-at-Risk Models, "Journal of Forecasting" 22, 337-358.
• [11] Tsay R.S., (2005), Analysis of Financial Time Series (2nd edition), Wiley, New York

Identyfikatory

DOI

10.24425/cejeme.2010.119331