IDEAS home Printed from https://ideas.repec.org/a/ibn/ibrjnl/v10y2017i11p88-102.html
   My bibliography  Save this article

The Role of the Skewed Distributions in the Framework of Extreme Value Theory (EVT)

Author

Listed:
  • Sonia Benito Muela
  • Carmen López-Martín
  • Mª Ángeles Navarro

Abstract

In this paper, we analyze the role of the heavy tail and skewed distribution in market risk estimation (Value at Risk (VaR)). In particular, we are interested in knowing if in the framework of the conditional extreme value theory, the estimation of the volatility model below heavy tail and skewed distribution contributes to improve the VaR estimation respect to these obtained from a symmetric distribution. The study has been carried out for six individual assets belonging to the digital sector: ADP, Amazon, Cerner, Apple, Microsoft and Telefonica. The analysis period runs from January 1st, 2008 to the end of December 2013. Although the evidence found is a little bit weak, the results obtained seem to indicate that the heavy tail and skewed distribution outperforms the symmetric distribution both in terms of accuracy VaR estimations as in terms of firm’s loss function. Furthermore, the market risk capital requirements fixed on the base of the VaR estimations are also lowest below a skewed distribution.

Suggested Citation

  • Sonia Benito Muela & Carmen López-Martín & Mª Ángeles Navarro, 2017. "The Role of the Skewed Distributions in the Framework of Extreme Value Theory (EVT)," International Business Research, Canadian Center of Science and Education, vol. 10(11), pages 88-102, November.
    • Handle: RePEc:ibn:ibrjnl:v:10:y:2017:i:11:p:88-102
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/ibr/article/view/71163/38922
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/ibr/article/view/71163/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael McAleer & Juan‐Ángel Jiménez‐Martín & Teodosio Pérez‐Amaral, 2013. "International Evidence on GFC‐Robust Forecasts for Risk Management under the Basel Accord," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(3), pages 267-288, April.
    2. Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio & Santos, Paulo Araújo, 2013. "GFC-robust risk management under the Basel Accord using extreme value methodologies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 223-237.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    5. Richard H. Gerlach & Cathy W. S. Chen & Nancy Y. C. Chan, 2011. "Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 481-492, October.
    6. 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.
    7. 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.).
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Cathy W.S. Chen & Richard Gerlach & Edward M. H. Lin & W. C. W. Lee, 2012. "Bayesian Forecasting for Financial Risk Management, Pre and Post the Global Financial Crisis," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 31(8), pages 661-687, December.
    10. 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.
    11. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
    12. 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.
    13. 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.
    14. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    15. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
    16. Arnold Polanski & Evarist Stoja, 2010. "Incorporating higher moments into value-at-risk forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(6), pages 523-535.
    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. Sonia Benito & Carmen López-Martín & Mª Ángeles Navarro, 2023. "Assessing the importance of the choice threshold in quantifying market risk under the POT approach (EVT)," Risk Management, Palgrave Macmillan, vol. 25(1), pages 1-31, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    2. Laura Garcia‐Jorcano & Alfonso Novales, 2021. "Volatility specifications versus probability distributions in VaR forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 189-212, March.
    3. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    4. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    5. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    6. 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.
    7. 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.
    8. Gerlach, Richard & Wang, Chao, 2020. "Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 489-506.
    9. Gonzalo Cortazar & Alejandro Bernales & Diether Beuermann, 2005. "Methodology and Implementation of Value-at-Risk Measures in Emerging Fixed-Income Markets with Infrequent Trading," Finance 0512030, University Library of Munich, Germany.
    10. Chang, Chia-Lin & González-Serrano, Lydia & Jimenez-Martin, Juan-Angel, 2013. "Currency hedging strategies using dynamic multivariate GARCH," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 164-182.
    11. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    12. Song, Shijia & Li, Handong, 2022. "Predicting VaR for China's stock market: A score-driven model based on normal inverse Gaussian distribution," International Review of Financial Analysis, Elsevier, vol. 82(C).
    13. Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio & Santos, Paulo Araújo, 2013. "GFC-robust risk management under the Basel Accord using extreme value methodologies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 223-237.
    14. Timotheos Angelidis & Stavros Degiannakis, 2007. "Backtesting VaR Models: An Expected Shortfall Approach," Working Papers 0701, University of Crete, Department of Economics.
    15. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    16. Abad, Pilar & Benito, Sonia, 2013. "A detailed comparison of value at risk estimates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 258-276.
    17. Laura Garcia-Jorcano & Alfonso Novales, 2020. "A dominance approach for comparing the performance of VaR forecasting models," Computational Statistics, Springer, vol. 35(3), pages 1411-1448, September.
    18. DAVID G. McMILLAN & ALAN E. H. SPEIGHT, 2007. "Value‐at‐Risk in Emerging Equity Markets: Comparative Evidence for Symmetric, Asymmetric, and Long‐Memory GARCH Models," International Review of Finance, International Review of Finance Ltd., vol. 7(1‐2), pages 1-19, March.
    19. Bayer, Sebastian, 2018. "Combining Value-at-Risk forecasts using penalized quantile regressions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 56-77.
    20. d’Addona, Stefano & Khanom, Najrin, 2022. "Estimating tail-risk using semiparametric conditional variance with an application to meme stocks," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 241-260.

    More about this item

    Keywords

    extreme value theory; loss functions; skewness distributions; value at risk;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    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:ibn:ibrjnl:v:10:y:2017:i:11:p:88-102. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.