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A Bayesian Confidence Interval for Value-at-Risk

Author

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  • Contreras, P.
  • Satchell, S.E.

Abstract

This study assesses the accuracy of the value-at-risk estimate (VaR). On the basis of posterior distributions of the unknown population parameters, we develop a confidence interval for VaR that reflects the genuine information available about the portfolios for which the VaR is calculated. This approach is more accurate than that in Dowd (2000) as it avoids explaining the behaviour of the population parameters on the basis of distributions of sample parameters. We find that the accuracy of both the confidence interval and the VaR estimate depend more dramatically on the sample size than what Dowd’s results suggest. In addition, we not only find that the impact of the confidence level and the holding period at which the VaR is predicated are negligible compared to that of the sample size (as in Dowd), but also that the confidence interval is far from being symmetric.

Suggested Citation

  • Contreras, P. & Satchell, S.E., 2003. "A Bayesian Confidence Interval for Value-at-Risk," Cambridge Working Papers in Economics 0348, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0348
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    References listed on IDEAS

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    1. Peter K. Cornelius, 2000. "Trade in Financial Services, Capital Flows, and the Value‐at‐Risk of Countries," The World Economy, Wiley Blackwell, vol. 23(5), pages 649-672, May.
    2. Karolyi, G. Andrew, 1993. "A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(4), pages 579-594, December.
    3. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    4. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
    5. Cornelius, Peter K., 2000. "Trade in financial services, capital flows, and the value-at-risk of countries," Research Notes 00-2, Deutsche Bank Research.
    6. Miss Liliana B Schumacher & Mr. Mario I. Bléjer, 1998. "Central Bank Vulnerability and the Credibility of Commitments: A Value-at-Risk Approach to Currency Crises," IMF Working Papers 1998/065, International Monetary Fund.
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    More about this item

    Keywords

    Bayesian Statistics; Confidence Interval; Monte Carlo Simulations; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G00 - Financial Economics - - General - - - General

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