IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1807.02422.html
   My bibliography  Save this paper

A Semi-parametric Realized Joint Value-at-Risk and Expected Shortfall Regression Framework

Author

Listed:
  • Chao Wang
  • Richard Gerlach
  • Qian Chen

Abstract

A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected Shortfall (ES) components, to jointly estimate and forecast VaR and ES. The measurement equation models the contemporaneous dependence between the realized measure (i.e., Realized Variance and Realized Range) and the latent conditional ES. An adaptive Bayesian Markov Chain Monte Carlo method is employed for estimation and forecasting, the properties of which are assessed and compared with maximum likelihood through a simulation study. In a comprehensive forecasting study on 1% and 2.5 % quantile levels, the proposed models are compared to a range of parametric, non-parametric and semi-parametric models, based on 7 market indices and 7 individual assets. One-day-ahead VaR and ES forecasting results favor the proposed models, especially when incorporating the sub-sampled Realized Variance and the sub-sampled Realized Range in the model.

Suggested Citation

  • Chao Wang & Richard Gerlach & Qian Chen, 2018. "A Semi-parametric Realized Joint Value-at-Risk and Expected Shortfall Regression Framework," Papers 1807.02422, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:1807.02422
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1807.02422
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    2. Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel R., 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 150-160.
    3. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    5. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    6. 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.).
    7. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. 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.
    10. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    11. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    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. Wilson Ye Chen & Gareth W. Peters & Richard H. Gerlach & Scott A. Sisson, 2017. "Dynamic Quantile Function Models," Papers 1707.02587, arXiv.org, revised May 2021.
    14. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    15. 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.
    16. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    17. Toshiaki Watanabe, 2012. "Quantile Forecasts Of Financial Returns Using Realized Garch Models," The Japanese Economic Review, Japanese Economic Association, vol. 63(1), pages 68-80, March.
    18. Richard Gerlach & Chao Wang, 2016. "Forecasting risk via realized GARCH, incorporating the realized range," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 501-511, April.
    19. 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.
    20. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
    21. Richard Gerlach & Cathy W. S. Chen, 2016. "Bayesian Expected Shortfall Forecasting Incorporating the Intraday Range," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 128-158.
    22. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    23. 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. Lazar, Emese & Xue, Xiaohan, 2020. "Forecasting risk measures using intraday data in a generalized autoregressive score framework," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1057-1072.

    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. Chao Wang & Richard Gerlach, 2019. "Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected Shortfall," Papers 1906.09961, arXiv.org.
    2. 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.
    3. Richard Gerlach & Chao Wang, 2016. "Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Realized Measures," Papers 1612.08488, arXiv.org.
    4. Vica Tendenan & Richard Gerlach & Chao Wang, 2020. "Tail risk forecasting using Bayesian realized EGARCH models," Papers 2008.05147, arXiv.org, revised Aug 2020.
    5. Chao Wang & Qian Chen & Richard Gerlach, 2017. "Bayesian Realized-GARCH Models for Financial Tail Risk Forecasting Incorporating Two-sided Weibull Distribution," Papers 1707.03715, arXiv.org.
    6. Richard Gerlach & Chao Wang, 2018. "Semi-parametric Dynamic Asymmetric Laplace Models for Tail Risk Forecasting, Incorporating Realized Measures," Papers 1805.08653, arXiv.org.
    7. Richard Gerlach & Chao Wang, 2016. "Forecasting risk via realized GARCH, incorporating the realized range," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 501-511, April.
    8. Lyócsa, Štefan & Todorova, Neda & Výrost, Tomáš, 2021. "Predicting risk in energy markets: Low-frequency data still matter," Applied Energy, Elsevier, vol. 282(PA).
    9. Tan, Shay-Kee & Ng, Kok-Haur & Chan, Jennifer So-Kuen & Mohamed, Ibrahim, 2019. "Quantile range-based volatility measure for modelling and forecasting volatility using high frequency data," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 537-551.
    10. David Happersberger & Harald Lohre & Ingmar Nolte, 2020. "Estimating portfolio risk for tail risk protection strategies," European Financial Management, European Financial Management Association, vol. 26(4), pages 1107-1146, September.
    11. Shay Kee Tan & Kok Haur Ng & Jennifer So-Kuen Chan, 2022. "Predicting Returns, Volatilities and Correlations of Stock Indices Using Multivariate Conditional Autoregressive Range and Return Models," Mathematics, MDPI, vol. 11(1), pages 1-24, December.
    12. Richard Gerlach & Declan Walpole & Chao Wang, 2017. "Semi-parametric Bayesian tail risk forecasting incorporating realized measures of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 199-215, February.
    13. Chen, Cathy W.S. & Hsu, Hsiao-Yun & Watanabe, Toshiaki, 2023. "Tail risk forecasting of realized volatility CAViaR models," Finance Research Letters, Elsevier, vol. 51(C).
    14. Dimitrios P. Louzis & Spyros Xanthopoulos‐Sisinis & Apostolos P. Refenes, 2013. "The Role of High‐Frequency Intra‐daily Data, Daily Range and Implied Volatility in Multi‐period Value‐at‐Risk Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 561-576, September.
    15. Beatriz Vaz de Melo Mendes & Victor Bello Accioly, 2017. "Improving (E)GARCH forecasts with robust realized range measures: Evidence from international markets," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 41(4), pages 631-658, October.
    16. F. Lilla, 2017. "High Frequency vs. Daily Resolution: the Economic Value of Forecasting Volatility Models - 2nd ed," Working Papers wp1099, Dipartimento Scienze Economiche, Universita' di Bologna.
    17. F. Lilla, 2016. "High Frequency vs. Daily Resolution: the Economic Value of Forecasting Volatility Models," Working Papers wp1084, Dipartimento Scienze Economiche, Universita' di Bologna.
    18. Lazar, Emese & Xue, Xiaohan, 2020. "Forecasting risk measures using intraday data in a generalized autoregressive score framework," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1057-1072.
    19. Trucíos, Carlos, 2019. "Forecasting Bitcoin risk measures: A robust approach," International Journal of Forecasting, Elsevier, vol. 35(3), pages 836-847.
    20. H. Rangika Iroshani Peiris & Chao Wang & Richard Gerlach & Minh-Ngoc Tran, 2024. "Semi-parametric financial risk forecasting incorporating multiple realized measures," Papers 2402.09985, arXiv.org.

    More about this item

    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:arx:papers:1807.02422. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.