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Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets

  • Sasa Zikovic
  • Randall Filer

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight from emerging markets) prior to and during the 2008 financial crisis. In addition to widely used VaR and ES models, we also study the behavior of conditional and unconditional extreme value (EV) models to generate 99 percent confidence level estimates as well as developing a new loss function that relates tail losses to ES forecasts. Backtesting results show that only our proposed new hybrid and Extreme Value (EV)-based VaR models provide adequate protection in both developed and emerging markets, but that the hybrid approach does this at a significantly lower cost in capital reserves. In ES estimation the hybrid model yields the smallest error statistics surpassing even the EV models, especially in the developed markets.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2820.

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Date of creation: 2009
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Handle: RePEc:ces:ceswps:_2820
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  1. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(1), pages 87-107, Winter.
  2. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304,
  3. John Cotter, 2004. "Downside risk for European equity markets," Applied Financial Economics, Taylor & Francis Journals, vol. 14(10), pages 707-716.
  4. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Center for Financial Institutions Working Papers 98-10, Wharton School Center for Financial Institutions, University of Pennsylvania.
  5. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
  6. Inui, Koji & Kijima, Masaaki, 2005. "On the significance of expected shortfall as a coherent risk measure," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 853-864, April.
  7. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
  8. Timotheos Angelidis & Stavros Degiannakis, 2007. "Backtesting VaR Models: An Expected Shortfall Approach," Working Papers 0701, University of Crete, Department of Economics.
  9. Gencay, Ramazan & Selcuk, Faruk, 2004. "Extreme value theory and Value-at-Risk: Relative performance in emerging markets," International Journal of Forecasting, Elsevier, vol. 20(2), pages 287-303.
  10. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  11. Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 227-255.
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