IDEAS home Printed from https://ideas.repec.org/p/pdn/ciepap/141.html
   My bibliography  Save this paper

Semiparametric GARCH models with long memory applied to Value at Risk and Expected Shortfall

Author

Listed:
  • Sebastian Letmathe

    (Paderborn University)

  • Yuanhua Feng

    (Paderborn University)

  • André Uhde

    (Paderborn University)

Abstract

In this paper new semiparametric GARCH models with long memory are in- troduced. The estimation of the nonparametric scale function is carried out by an adapted version of the SEMIFAR algorithm (Beran et al., 2002). Recurring on the revised recommendations by the Basel Committee to measure market risk in the banks' trading books (Basel Committee on Banking Supervision, 2013), the semi- parametric GARCH models are applied to obtain rolling one-step ahead forecasts for the Value at Risk (VaR) and Expected Shortfall (ES) for market risk assets. In addition, standard regulatory traffic light tests (Basel Committee on Banking Supervision, 1996) and a newly introduced traffic light test for the ES are carried out for all models. The practical relevance of our proposal is demonstrated by a comparative study. Our results indicate that semiparametric long memory GARCH models are an attractive alternative to their conventional, parametric counterparts.

Suggested Citation

  • Sebastian Letmathe & Yuanhua Feng & André Uhde, 2021. "Semiparametric GARCH models with long memory applied to Value at Risk and Expected Shortfall," Working Papers CIE 141, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:141
    as

    Download full text from publisher

    File URL: http://groups.uni-paderborn.de/wp-wiwi/RePEc/pdf/ciepap/WP141.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. 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.
    4. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    5. 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.
    6. Chaker Aloui & Hela BEN HAMIDA, 2015. "Estimation and Performance Assessment of Value-at-Risk and Expected Shortfall Based on Long-Memory GARCH-Class Models," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 65(1), pages 30-54, January.
    7. Grané, A. & Veiga, H., 2008. "Accurate minimum capital risk requirements: A comparison of several approaches," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2482-2492, November.
    8. Demiralay, Sercan & Ulusoy, Veysel, 2014. "Value-at-risk Predictions of Precious Metals with Long Memory Volatility Models," MPRA Paper 53229, University Library of Munich, Germany.
    9. Michel Beine & Sebastien Laurent & Christelle Lecourt, 2002. "Accounting for conditional leptokurtosis and closing days effects in FIGARCH models of daily exchange rates," Applied Financial Economics, Taylor & Francis Journals, vol. 12(8), pages 589-600.
    10. Härdle, Wolfgang Karl & Mungo, Julius, 2008. "Value-at-risk and expected shortfall when there is long range dependence," SFB 649 Discussion Papers 2008-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    12. Susan Thomas & Mandira Sarma & Ajay Shah, 2003. "Selection of Value-at-Risk models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(4), pages 337-358.
    13. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    14. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
    15. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    16. repec:hum:wpaper:sfb649dp2008-006 is not listed on IDEAS
    17. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    18. 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.
    19. Jan Beran & Yuanhua Feng & Sucharita Ghosh, 2015. "Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models," Statistical Papers, Springer, vol. 56(2), pages 431-451, May.
    20. Stavros Degiannakis, 2004. "Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model," Applied Financial Economics, Taylor & Francis Journals, vol. 14(18), pages 1333-1342.
    21. Nick Costanzino & Michael Curran, 2018. "A Simple Traffic Light Approach to Backtesting Expected Shortfall," Risks, MDPI, vol. 6(1), pages 1-7, January.
    22. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    23. Beran, Jan & Ocker, Dirk, 1999. "SEMIFAR Forecasts, with Applications to Foreign Exchange Rates," CoFE Discussion Papers 99/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    24. Yuanhua Feng & Jan Beran & Sebastian Letmathe & Sucharita Ghosh, 2020. "Fractionally integrated Log-GARCH with application to value at risk and expected shortfall," Working Papers CIE 137, Paderborn University, CIE Center for International Economics.
    25. 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)

    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. Yuanhua Feng & Jan Beran & Sebastian Letmathe & Sucharita Ghosh, 2020. "Fractionally integrated Log-GARCH with application to value at risk and expected shortfall," Working Papers CIE 137, Paderborn University, CIE Center for International Economics.
    2. Geoffrey Ngene & Kenneth A. Tah & Ali F. Darrat, 2017. "Long memory or structural breaks: Some evidence for African stock markets," Review of Financial Economics, John Wiley & Sons, vol. 34(1), pages 61-73, September.
    3. Geoffrey Ngene & Ann Nduati Mungai & Allen K. Lynch, 2018. "Long-Term Dependency Structure and Structural Breaks: Evidence from the U.S. Sector Returns and Volatility," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-38, June.
    4. Degiannakis, Stavros & Floros, Christos & Dent, Pamela, 2013. "Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence," International Review of Financial Analysis, Elsevier, vol. 27(C), pages 21-33.
    5. Aloui, Chaker & Hamida, Hela ben, 2014. "Modelling and forecasting value at risk and expected shortfall for GCC stock markets: Do long memory, structural breaks, asymmetry, and fat-tails matter?," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 349-380.
    6. repec:awi:wpaper:0472 is not listed on IDEAS
    7. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    8. Chkili, Walid & Aloui, Chaker & Nguyen, Duc Khuong, 2012. "Asymmetric effects and long memory in dynamic volatility relationships between stock returns and exchange rates," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(4), pages 738-757.
    9. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    10. Feng, Yuanhua & Härdle, Wolfgang Karl, 2020. "A data-driven P-spline smoother and the P-Spline-GARCH models," IRTG 1792 Discussion Papers 2020-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. 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.
    12. Cheong, Chin Wen, 2009. "Modeling and forecasting crude oil markets using ARCH-type models," Energy Policy, Elsevier, vol. 37(6), pages 2346-2355, June.
    13. Timotheos Angelidis & Stavros Degiannakis, 2007. "Backtesting VaR Models: An Expected Shortfall Approach," Working Papers 0701, University of Crete, Department of Economics.
    14. David McMillan & Raquel Quiroga Garcia, 2009. "Intra-day volatility forecasts," Applied Financial Economics, Taylor & Francis Journals, vol. 19(8), pages 611-623.
    15. Nigel Wilkins, 2004. "Indirect Estimation of Long Memory Volatility Models," Econometric Society 2004 Far Eastern Meetings 459, Econometric Society.
    16. Sebastian Letmathe & Jan Beran & Yuanhua Feng, 2024. "An extended exponential SEMIFAR model with application in R," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(22), pages 7914-7926, November.
    17. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    18. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, November.
    19. Arteche, Josu, 2004. "Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models," Journal of Econometrics, Elsevier, vol. 119(1), pages 131-154, March.
    20. Onder Buberkoku, 2018. "Examining the Value-at-risk Performance of Fractionally Integrated GARCH Models: Evidence from Energy Commodities," International Journal of Economics and Financial Issues, Econjournals, vol. 8(3), pages 36-50.
    21. Yanlin Shi & Yang Yang, 2018. "Modeling High Frequency Data with Long Memory and Structural Change: A-HYEGARCH Model," Risks, MDPI, vol. 6(2), pages 1-28, March.

    More about this item

    Keywords

    Semiparametric; long memory; GARCH models; forecasting; Value at Risk; Expected Shortfall; traffic light test; Basel Committee on Banking Supervision;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pdn:ciepap:141. 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: WP-WiWi-Info The email address of this maintainer does not seem to be valid anymore. Please ask WP-WiWi-Info to update the entry or send us the correct address or the person in charge The email address of this maintainer does not seem to be valid anymore. Please ask the person in charge to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/cipadde.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.