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The hidden dangers of historical simulation

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Author Info
Matthew Pritsker
Abstract

Many large financial institutions compute the Value-at-Risk (VaR) of their trading portfolios using historical simulation based methods, but the methods' properties are not well understood. This paper theoretically and empirically examines the historical simulation method, a variant of historical simulation introduced by Boudoukh, Richardson and Whitelaw (1998) (BRW), and the Filtered Historical Simulation method (FHS) of Barone-Adesi, Giannopoulos, and Vosper (1999). The Historical Simulation and BRW methods are both under-responsive to changes in conditional risk; and respond to changes in risk in an asymmetric fashion: measured risk increases when the portfolio experiences large losses, but not when it earns large gains. The FHS method appears promising, but requires additional refinement to account for time-varying correlations; and to choose the appropriate length of historical sample period. Preliminary analysis suggests that 2 years of daily data may not contain enough extreme outliers to accurately compute 1% VaR at a 10-day horizon using the FHS method.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2001-27.

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Date of creation: 2001
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Handle: RePEc:fip:fedgfe:2001-27

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Keywords: Risk ; Econometric models;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer, vol. 12(2), pages 201-242, October. [Downloadable!] (restricted)
  2. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663. [Downloadable!]
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  3. Robert Engle & Simone Manganelli, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series 1999-20, Department of Economics, UC San Diego. [Downloadable!]
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  4. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  5. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  7. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Georges Dionne & Pierre Duchesne & Maria Pacurar, 2005. "Intraday Value at Risk (IVaR) Using Tick-by-Tick Data with Application to the Toronto Stock Exchange," Cahiers de recherche 0533, CIRPEE. [Downloadable!]
  2. Gaglianone, Wagner Piazza & Linton, Oliver & Lima, Luiz Renato Regis de Oliveira, 2008. "Evaluating Value-at-Risk models via Quantile regressions," Economics Working Papers (Ensaios Economicos da EPGE) 679, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
  3. Peter Christoffersen & Sílvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO. [Downloadable!]
  4. Sean D. Campbell, 2005. "A review of backtesting and backtesting procedures," Finance and Economics Discussion Series 2005-21, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  5. Michael S. Gibson, 2001. "Incorporating event risk into value-at-risk," Finance and Economics Discussion Series 2001-17, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  6. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," CFS Working Paper Series 2005/02, Center for Financial Studies. [Downloadable!]
    Other versions:
  7. Scheicher, Martin & Raunig, Burkhard, 2008. "A value at risk analysis of credit default swaps," Discussion Paper Series 2: Banking and Financial Studies 2008,12, Deutsche Bundesbank, Research Centre. [Downloadable!]
  8. Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO. [Downloadable!]
    Other versions:
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