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Econometric modeling and value-at-risk using the Pearson type-IV distribution

Author

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  • Stavroyiannis, S.
  • Makris, I.
  • Nikolaidis, V.
  • Zarangas, L.

Abstract

The recent financial crisis of 2007–2009 has challenged the requirements of Basel II agreement on capital adequacy as well as, the appropriateness of value-at-risk (VaR) measurement for properly “back-tested” and “stress-tested” models. This paper reconsiders the use of VaR as a measure for potential risk of economic losses in financial markets. We incorporate a GARCH model where the innovation process follows the Pearson-IV distribution, and the results are compared with the skewed Student-t distribution, in the sense of Fernandez and Steel. As case studies we consider the major historical indices of daily returns, DJIA, NASDAQ Composite, FTSE100, CAC40, DAX, and S&P500. VaR and backtesting are performed by the success–failure ratio, the Kupiec LR test, the Christoffersen independence and conditional coverage tests, the expected shortfall with ESF1 and ESF2 measures, and the dynamic quantile test of Engle and Manganelli. The main findings indicate that the Pearson type-IV distribution gives better results, compared with the skewed student distribution, especially at the high confidence levels, providing a very good candidate as an alternative distributional scheme.

Suggested Citation

  • Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    • Handle: RePEc:eee:finana:v:22:y:2012:i:c:p:10-17
    DOI: 10.1016/j.irfa.2012.02.003
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    6. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2017. "Risk quantification in turmoil markets," Risk Management, Palgrave Macmillan, vol. 19(3), pages 202-224, August.
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    8. Stavros Stavroyiannis, 2017. "A note on the Nelson Cao inequality constraints in the GJR-GARCH model: Is there a leverage effect?," Papers 1705.00535, arXiv.org.
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    10. Sree Vinutha Venkataraman & S. V. D. Nageswara Rao, 2016. "Estimation of dynamic VaR using JSU and PIV distributions," Risk Management, Palgrave Macmillan, vol. 18(2), pages 111-134, August.
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    More about this item

    Keywords

    Financial markets; Value-at-risk; GARCH model; Pearson type-IV distribution;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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