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Value-at-Risk and Extreme Returns

Author

Listed:
  • Jón Daníelsson

    (London School of Economics, University of Iceland)

  • Casper G. de Vries

    (Erasmus University Rotterdam)

Abstract

Accurate prediction of the frequency of extreme events is of primary importance in many financialapplications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaRevaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non-parametric empirical distribution function. The semi-parametric method is compared with historicalsimulation and the J.P. Morgan RiskMetrics technique on a portfolio of stock returns. For predictions oflow probability worst outcomes, RiskMetrics analysis underpredicts the VaR while historical simulationoverpredicts the VaR. However, the estimates obtained from applying the semi-parametric method aremore accurate in the VaR prediction. In addition, an option is used in the portfolio to lower downsiderisk. Finally, it is argued that current regulatory environment provides incentives to use the lowestquality VaR method available.

Suggested Citation

  • Jón Daníelsson & Casper G. de Vries, 1998. "Value-at-Risk and Extreme Returns," Tinbergen Institute Discussion Papers 98-017/2, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19980017
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    References listed on IDEAS

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    1. de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
    2. J. S. Butler & Barry Schachter, 1996. "Improving Value-At-Risk Estimates By Combining Kernel Estimation With Historical Simulation," Finance 9605001, University Library of Munich, Germany.
    3. J. S. Butler & Barry Schachter, 1996. "Improving value-at-risk estimates by combining kernel estimation," Proceedings 513, Federal Reserve Bank of Chicago.
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    JEL classification:

    • G00 - Financial Economics - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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