IDEAS home Printed from https://ideas.repec.org/a/eee/finana/v22y2012icp10-17.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S105752191200018X
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Stambaugh, Fred, 1996. "Risk and value at risk," European Management Journal, Elsevier, vol. 14(6), pages 612-621, December.
    5. Fielitz, Bruce D., 1971. "Stationarity of Random Data: Some Implications for the Distribution of Stock Price Changes," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(03), pages 1025-1034, June.
    6. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    8. 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.).
    9. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    10. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393-393.
    11. Bhattacharyya, Malay & Chaudhary, Abhishek & Yadav, Gaurav, 2008. "Conditional VaR estimation using Pearson's type IV distribution," European Journal of Operational Research, Elsevier, vol. 191(2), pages 386-397, December.
    12. 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.
    13. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Yu Chuan Huang & Bor-Jing Lin, 2004. "Value-at-Risk Analysis for Taiwan Stock Index Futures: Fat Tails and Conditional Asymmetries in Return Innovations," Review of Quantitative Finance and Accounting, Springer, vol. 22(2), pages 79-95, March.
    16. Matteo Grigoletto & Francesco Lisi, 2011. "Practical implications of higher moments in risk management," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(4), pages 487-506, November.
    17. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    18. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    19. Tang, Ta-Lun & Shieh, Shwu-Jane, 2006. "Long memory in stock index futures markets: A value-at-risk approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 437-448.
    20. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Proceedings 512, Federal Reserve Bank of Chicago.
    21. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    22. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    23. Anastassios A. Drakos & Georgios P. Kouretas & Leonidas P. Zarangas, 2010. "Forecasting financial volatility of the Athens stock exchange daily returns: an application of the asymmetric normal mixture GARCH model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(4), pages 331-350.
    24. Kurt Brannas & Niklas Nordman, 2003. "Conditional skewness modelling for stock returns," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 725-728.
    25. Gamini Premaratne, 2005. "A Test for Symmetry with Leptokurtic Financial Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 169-187.
    26. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9-10), pages 1586-1609.
    27. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    28. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 84-108.
    29. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    30. Nagahara, Yuichi, 2004. "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 1-29, August.
    31. 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 841-862, November.
    32. Matteo Grigoletto & Francesco Lisi, 2009. "Looking for skewness in financial time series," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 310-323, July.
    33. McMillan, David G. & Kambouroudis, Dimos, 2009. "Are RiskMetrics forecasts good enough? Evidence from 31 stock markets," International Review of Financial Analysis, Elsevier, vol. 18(3), pages 117-124, June.
    34. Laurent, Sebastien & Peters, Jean-Philippe, 2002. " G@RCH 2.2: An Ox Package for Estimating and Forecasting Various ARCH Models," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 447-485, July.
    35. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc.
    36. Y. K. Tse, 1998. "The conditional heteroscedasticity of the yen-dollar exchange rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 49-55.
    37. Diamandis, Panayiotis F. & Drakos, Anastassios A. & Kouretas, Georgios P. & Zarangas, Leonidas, 2011. "Value-at-risk for long and short trading positions: Evidence from developed and emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 20(3), pages 165-176, June.
    38. Stavroyiannis, S. & Makris, I. & Nikolaidis, V., 2010. "Non-extensive properties, multifractality, and inefficiency degree of the Athens Stock Exchange General Index," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 19-24, January.
    39. Nagahara, Yuichi, 1999. "The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 251-264, July.
    40. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stavros Stavroyiannis & Leonidas Zarangas, 2013. "Out of Sample Value-at-Risk and Backtesting with the Standardized Pearson Type-IV Skewed Distribution," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 60(2), pages 231-247, April.
    2. 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.
    3. Stavros Stavroyiannis, 2016. "Value-at-Risk and backtesting with the APARCH model and the standardized Pearson type IV distribution," Papers 1602.05749, arXiv.org.

    More about this item

    Keywords

    Financial markets; Value-at-risk; GARCH model; Pearson type-IV distribution;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:finana:v:22:y:2012:i:c:p:10-17. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/620166 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.