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Varying the VaR for Unconditional and Conditional Environments

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  • Cotter, John

Abstract

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3483.

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Date of creation: 2004
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Handle: RePEc:pra:mprapa:3483

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  1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-081, New York University, Leonard N. Stern School of Business-.
  2. Pownall, Rachel A. J. & Koedijk, Kees G., 1999. "Capturing downside risk in financial markets: the case of the Asian Crisis," Journal of International Money and Finance, Elsevier, vol. 18(6), pages 853-870, December.
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  4. Cotter, John, 2001. "Margin exceedences for European stock index futures using extreme value theory," Journal of Banking & Finance, Elsevier, vol. 25(8), pages 1475-1502, August.
  5. Peter C.B. Phillips & James W. McFarland & Patrick C. McMahon, 1994. "Robust Tests of Forward Exchange Market Efficiency with Empirical Evidence from the 1920's," Cowles Foundation Discussion Papers 1080, Cowles Foundation for Research in Economics, Yale University.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-060, New York University, Leonard N. Stern School of Business-.
  7. Peter F. Christoffersen & Francis X. Diebold, 1997. "How Relevant is Volatility Forecasting for Financial Risk Management?," Center for Financial Institutions Working Papers 97-45, Wharton School Center for Financial Institutions, University of Pennsylvania.
  8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  9. 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.
  10. Huisman, Ronald & Koedijk, Kees G. & Kool, Clemens J.M. & Palm, Franz, 2001. "Tail-index estimates in small samples," Open Access publications from Maastricht University urn:nbn:nl:ui:27-5756, Maastricht University.
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  12. Ghose, Devajyoti & Kroner, Kenneth F., 1995. "The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 225-251, September.
  13. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
  14. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
  15. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
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  19. Giovanni Barone-Adesi & Kostas Giannopoulos & Les Vosper, 2002. "Backtesting Derivative Portfolios with Filtered Historical Simulation (FHS)," European Financial Management, European Financial Management Association, vol. 8(1), pages 31-58.
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Cited by:
  1. Cotter, John & Dowd, Kevin, 2007. "The tail risks of FX return distributions: A comparison of the returns associated with limit orders and market orders," Finance Research Letters, Elsevier, vol. 4(3), pages 146-154, September.
  2. Cotter, John & Dowd, Kevin & Morgan, C. Wyn, 2008. "Extreme Measures of Agricultural Financial Risk," Miscellaneous Papers 101971, Agecon Search.
  3. John Cotter & Kevin Dowd, 2011. "Intra-Day Seasonality in Foreign Market Transactions," Working Papers 200744, Geary Institute, University College Dublin.
  4. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
  5. Christian Francq & Jean-Michel Zakoïan, 2011. "Estimating the Marginal Law of a Time Series with Applications to Heavy Tailed Distributions," Working Papers 2011-30, Centre de Recherche en Economie et Statistique.
  6. Kevin Dowd & John Cotter, 2011. "Spectral Risk Measures with an Application to Futures Clearinghouse Variation Margin Requirements," Working Papers 200742, Geary Institute, University College Dublin.
  7. Trenca Ioan & Zoicas-Ienciu Adrian, 2010. "The Correlation Between The Market Risk And The Liquidity Risk In The Romanian Banking Sector," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 437-442, July.

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