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Value-at-Risk and Expected Shortfall when there is long range dependence

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Author Info
Wolfgang Härdle
Julius Mungo

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Abstract

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and forecasting of market volatility. The implication is that models that accomodate long memory hold the promise of improved long-run volatility forecast as well as accurate pricing of long-term contracts. On the other hand, recent focus is on whether long memory can affect the measurement of market risk in the context of Value-at- Risk (V aR). In this paper, we evaluate the Value-at-Risk (V aR) and Expected Shortfall (ESF) in financial markets under such conditions. We examine one equity portfolio, the British FTSE100 and three stocks of the German DAX index portfolio (Bayer, Siemens and Volkswagen). Classical V aR estimation methodology such as exponential moving average (EMA) as well as extension to cases where long memory is an inherent characteristics of the system are investigated. In particular, we estimate two long memory models, the Fractional Integrated Asymmetric Power-ARCH and the Hyperbolic-GARCH with different error distribution assumptions. Our results show that models that account for asymmetries in the volatility specifications as well as fractional integrated parametrization of the volatility process, perform better in predicting the one-step as well as five-step ahead V aR and ESF for short and long positions than short memory models. This suggests that for proper risk valuation of options, the degree of persistence should be investigated and appropriate models that incorporate the existence of such characteristic be taken into account.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2008-006.

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Length: 40 pages
Date of creation: Jan 2008
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Handle: RePEc:hum:wpaper:sfb649dp2008-006

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Related research
Keywords: Backtesting Value-at-Risk Expected Shortfall Long Memory Fractional Integrated Volatility Models

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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References listed on IDEAS
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. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July. [Downloadable!] (restricted)
    Other versions:
  2. Stavros Degiannakis, 2004. "Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model," Applied Financial Economics, Taylor and Francis Journals, vol. 14(18), pages 1333-1342, December. [Downloadable!] (restricted)
  3. Liudas Giraitis & Piotr Kokoszka & Remigijus Leipus & Gilles Teyssière, 2000. "Semiparametric Estimation of the Intensity of Long Memory in Conditional Heteroskedasticity," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 113-128, January. [Downloadable!] (restricted)
  4. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June. [Downloadable!] (restricted)
    Other versions:
  5. Robinson, P.M. & Henry, M., 1999. "Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels," Econometric Theory, Cambridge University Press, vol. 15(03), pages 299-336, June. [Downloadable!]
  6. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, issue Apr, pages 39-69. [Downloadable!]
  7. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Blackwell Publishing, vol. 14(1), pages 115-129. [Downloadable!] (restricted)
  8. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Proceedings, Federal Reserve Bank of Chicago, issue May, pages 334-362.
  9. Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 531-554, December. [Downloadable!] (restricted)
  10. Henry, Olan T, 2002. "Long Memory in Stock Returns: Some International Evidence," Applied Financial Economics, Taylor and Francis Journals, vol. 12(10), pages 725-29, October. [Downloadable!] (restricted)
  11. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation, Yale University. [Downloadable!]
  12. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February. [Downloadable!]
  13. So, Mike K P, 2000. "Long-Term Memory in Stock Market Volatility," Applied Financial Economics, Taylor and Francis Journals, vol. 10(5), pages 519-24, October. [Downloadable!] (restricted)
  14. Jurgen Doornik & Marius Ooms, 2004. "Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 8(2), pages 1218-1218. [Downloadable!] (restricted)
  15. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October. [Downloadable!] (restricted)
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Cited by:
(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. Enzo Giacomini & Wolfgang Härdle & Volker Krätschmer, 2008. "Dynamic Semiparametric Factor Models in Risk Neutral Density Estimation," SFB 649 Discussion Papers SFB649DP2008-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Nikolaus Hautsch & Dieter Hess & Christoph Müller, 2008. "Price Adjustment to News with Uncertain Precision," SFB 649 Discussion Papers SFB649DP2008-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  3. Viktor Winschel & Markus Krätzig, 2008. "JBendge: An Object-Oriented System for Solving, Estimating and Selecting Nonlinear Dynamic Models," SFB 649 Discussion Papers SFB649DP2008-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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