IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v6y2018i2p45-d142858.html
   My bibliography  Save this article

Estimating and Forecasting Conditional Risk Measures with Extreme Value Theory: A Review

Author

Listed:
  • Marco Bee

    (Department of Economics and Management, University of Trento, via Inama 5, 38122 Trento, Italy)

  • Luca Trapin

    (Department of Mathematical Sciences, Mathematical Finance and Econometrics, Università Cattolica del Sacro Cuore, Largo Gemelli 1, 20123 Milano, Italy)

Abstract

One of the key components of financial risk management is risk measurement. This typically requires modeling, estimating and forecasting tail-related quantities of the asset returns’ conditional distribution. Recent advances in the financial econometrics literature have developed several models based on Extreme Value Theory (EVT) to carry out these tasks. The purpose of this paper is to review these methods.

Suggested Citation

  • Marco Bee & Luca Trapin, 2018. "Estimating and Forecasting Conditional Risk Measures with Extreme Value Theory: A Review," Risks, MDPI, vol. 6(2), pages 1-16, April.
  • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:45-:d:142858
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/6/2/45/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-9091/6/2/45/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    2. Herrera, Rodrigo & Schipp, Bernhard, 2013. "Value at risk forecasts by extreme value models in a conditional duration framework," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 33-47.
    3. Chavez-Demoulin, V. & McGill, J.A., 2012. "High-frequency financial data modeling using Hawkes processes," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3415-3426.
    4. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    7. Marco Bee & Debbie J. Dupuis & Luca Trapin, 2018. "Realized extreme quantile: A joint model for conditional quantiles and measures of volatility with EVT refinements," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 398-415, April.
    8. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    9. Luca Trapin, 2018. "Can Volatility Models Explain Extreme Events?," Journal of Financial Econometrics, Oxford University Press, vol. 16(2), pages 297-315.
    10. Herrera, R. & Clements, A.E., 2018. "Point process models for extreme returns: Harnessing implied volatility," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 161-175.
    11. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    12. Marco Rocco, 2014. "Extreme Value Theory In Finance: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 28(1), pages 82-108, February.
    13. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    14. Filip Žikeš & Jozef Baruník, 2016. "Semi-parametric Conditional Quantile Models for Financial Returns and Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 185-226.
    15. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    16. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    17. Araújo Santos, Paulo & Fraga Alves, Isabel & Hammoudeh, Shawkat, 2013. "High quantiles estimation with Quasi-PORT and DPOT: An application to value-at-risk for financial variables," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 487-496.
    18. 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.
    19. Yi, Yanping & Feng, Xingdong & Huang, Zhuo, 2014. "Estimation of extreme value-at-risk: An EVT approach for quantile GARCH model," Economics Letters, Elsevier, vol. 124(3), pages 378-381.
    20. V. Chavez-Demoulin & A. C. Davison & A. J. McNeil, 2005. "Estimating value-at-risk: a point process approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 227-234.
    21. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    22. Rodrigo Herrera & Bernhard Schipp, 2011. "Extreme value models in a conditional duration intensity framework," SFB 649 Discussion Papers SFB649DP2011-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    23. 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.
    24. James W. Taylor & Keming Yu, 2016. "Using auto-regressive logit models to forecast the exceedance probability for financial risk management," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(4), pages 1069-1092, October.
    25. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    26. Araújo Santos, P. & Fraga Alves, M.I., 2013. "Forecasting Value-at-Risk with a duration-based POT method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 295-309.
    27. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556, May.
    28. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    29. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89.
    30. 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.
    31. Chavez-Demoulin, V. & Embrechts, P. & Sardy, S., 2014. "Extreme-quantile tracking for financial time series," Journal of Econometrics, Elsevier, vol. 181(1), pages 44-52.
    32. Andrew J. Patton & Kevin Sheppard, 2015. "Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility," The Review of Economics and Statistics, MIT Press, vol. 97(3), pages 683-697, July.
    33. Daniele Massacci, 2017. "Tail Risk Dynamics in Stock Returns: Links to the Macroeconomy and Global Markets Connectedness," Management Science, INFORMS, vol. 63(9), pages 3072-3089, September.
    34. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    35. 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.
    36. Bee, Marco & Dupuis, Debbie J. & Trapin, Luca, 2016. "Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 86-99.
    37. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    38. Schaumburg, Julia, 2012. "Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4081-4096.
    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. Osman Doğan & Süleyman Taşpınar & Anil K. Bera, 2021. "Bayesian estimation of stochastic tail index from high-frequency financial data," Empirical Economics, Springer, vol. 61(5), pages 2685-2711, November.
    2. Hamed Tabasi & Vahidreza Yousefi & Jolanta Tamošaitienė & Foroogh Ghasemi, 2019. "Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models," Administrative Sciences, MDPI, vol. 9(2), pages 1-17, May.
    3. Katleho Makatjane & Ntebogang Moroke, 2021. "Predicting Extreme Daily Regime Shifts in Financial Time Series Exchange/Johannesburg Stock Exchange—All Share Index," IJFS, MDPI, vol. 9(2), pages 1-18, 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. Fuentes, Fernanda & Herrera, Rodrigo & Clements, Adam, 2023. "Forecasting extreme financial risk: A score-driven approach," International Journal of Forecasting, Elsevier, vol. 39(2), pages 720-735.
    3. Hoga, Yannick, 2021. "The uncertainty in extreme risk forecasts from covariate-augmented volatility models," International Journal of Forecasting, Elsevier, vol. 37(2), pages 675-686.
    4. James, Robert & Leung, Henry & Leung, Jessica Wai Yin & Prokhorov, Artem, 2023. "Forecasting tail risk measures for financial time series: An extreme value approach with covariates," Journal of Empirical Finance, Elsevier, vol. 71(C), pages 29-50.
    5. 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.
    6. Louzis, Dimitrios P. & Xanthopoulos-Sisinis, Spyros & Refenes, Apostolos P., 2011. "Are realized volatility models good candidates for alternative Value at Risk prediction strategies?," MPRA Paper 30364, University Library of Munich, Germany.
    7. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    8. Bee, Marco & Dupuis, Debbie J. & Trapin, Luca, 2016. "Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 86-99.
    9. Wilson Calmon & Eduardo Ferioli & Davi Lettieri & Johann Soares & Adrian Pizzinga, 2021. "An Extensive Comparison of Some Well‐Established Value at Risk Methods," International Statistical Review, International Statistical Institute, vol. 89(1), pages 148-166, April.
    10. Song, Shijia & Tian, Fei & Li, Handong, 2021. "An intraday-return-based Value-at-Risk model driven by dynamic conditional score with censored generalized Pareto distribution," Journal of Asian Economics, Elsevier, vol. 74(C).
    11. Benjamin Mögel & Benjamin R. Auer, 2018. "How accurate are modern Value-at-Risk estimators derived from extreme value theory?," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 979-1030, May.
    12. 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.
    13. Nieto, María Rosa & Ruiz Ortega, Esther, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Wu, Qi & Yan, Xing, 2019. "Capturing deep tail risk via sequential learning of quantile dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    15. Chao Wang & Richard Gerlach, 2019. "Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected Shortfall," Papers 1906.09961, arXiv.org.
    16. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    17. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3498-3516.
    18. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    19. Hua, Jian & Manzan, Sebastiano, 2013. "Forecasting the return distribution using high-frequency volatility measures," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4381-4403.
    20. Giovanni Bonaccolto & Massimiliano Caporin, 2016. "The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective," JRFM, MDPI, vol. 9(3), pages 1-25, July.

    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:gam:jrisks:v:6:y:2018:i:2:p:45-:d:142858. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.