IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v30y2021i3d10.1007_s10260-020-00550-6.html
   My bibliography  Save this article

Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution

Author

Listed:
  • Marco Bottone

    (Banca d’Italia)

  • Lea Petrella

    (Sapienza University of Rome)

  • Mauro Bernardi

    (University of Padua)

Abstract

Conditional Autoregressive Value-at-Risk and Conditional Autoregressive Expectile have become two popular approaches for direct measurement of market risk. Since their introduction several improvements both in the Bayesian and in the classical framework have been proposed to better account for asymmetry and local non-linearity. Here we propose a unified Bayesian Conditional Autoregressive Risk Measures approach by using the Skew Exponential Power distribution. Further, we extend the proposed models using a semiparametric P-Spline approximation answering for a flexible way to consider the presence of non-linearity. To make the statistical inference we adapt the MCMC algorithm proposed in Bernardi et al. (2018) to our case. The effectiveness of the whole approach is demonstrated using real data on daily return of five stock market indices.

Suggested Citation

  • Marco Bottone & Lea Petrella & Mauro Bernardi, 2021. "Unified Bayesian conditional autoregressive risk measures using the skew exponential power distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1079-1107, September.
  • Handle: RePEc:spr:stmapp:v:30:y:2021:i:3:d:10.1007_s10260-020-00550-6
    DOI: 10.1007/s10260-020-00550-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-020-00550-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10260-020-00550-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gerlach, Richard H. & Chen, Cathy W. S. & Chan, Nancy Y. C., 2011. "Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 481-492.
    2. Chen, Cathy W.S. & Gerlach, Richard & Lin, Liou-Yan, 2012. "Bayesian Semi-parametric Expected Shortfall Forecasting in Financial M arkets," Working Papers 12 BAWP, University of Sydney Business School, Discipline of Business Analytics.
    3. 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.
    4. 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.
    5. Cathy Chen & Simon Lin & Philip Yu, 2012. "Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 19-48, June.
    6. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    7. Gerlach, Richard & Wang, Chao, 2015. "Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Range and Realized Measures," Working Papers 2015-07, University of Sydney Business School, Discipline of Business Analytics.
    8. Zhu, Dongming & Zinde-Walsh, Victoria, 2009. "Properties and estimation of asymmetric exponential power distribution," Journal of Econometrics, Elsevier, vol. 148(1), pages 86-99, January.
    9. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    10. 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.).
    11. Brezger, Andreas & Steiner, Winfried J., 2008. "Monotonic Regression Based on Bayesian PSplines: An Application to Estimating Price Response Functions From Store-Level Scanner Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 90-104, January.
    12. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
    13. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    14. Cathy W. S. Chen & Mike K. P. So & Edward M. H. Lin, 2009. "Volatility forecasting with double Markov switching GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 681-697.
    15. 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.
    16. Athanasios Kottas & Milovan Krnjajić, 2009. "Bayesian Semiparametric Modelling in Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 297-319, June.
    17. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    18. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    19. 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.
    20. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    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. Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Expectile hidden Markov regression models for analyzing cryptocurrency returns," Papers 2301.09722, arXiv.org, revised Jan 2024.
    2. Beatrice Foroni & Luca Merlo & Lea Petrella, 2023. "Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market," Papers 2307.06400, arXiv.org.
    3. Fabrizio Leisen & Luca Rossini & Cristiano Villa, 2020. "Loss-based approach to two-piece location-scale distributions with applications to dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 309-333, June.

    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. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    2. Merlo, Luca & Petrella, Lea & Raponi, Valentina, 2021. "Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation," Journal of Banking & Finance, Elsevier, vol. 133(C).
    3. 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.
    4. Derek Bunn, Arne Andresen, Dipeng Chen, Sjur Westgaard, 2016. "Analysis and Forecasting of Electricty Price Risks with Quantile Factor Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    5. Luca Merlo & Lea Petrella & Valentina Raponi, 2021. "Forecasting VaR and ES using a joint quantile regression and implications in portfolio allocation," Papers 2106.06518, arXiv.org.
    6. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
    7. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    8. Antonio Rubia Serrano & Lidia Sanchis-Marco, 2015. "Measuring Tail-Risk Cross-Country Exposures in the Banking Industry," Working Papers. Serie AD 2015-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. 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.
    10. Chao Wang & Richard Gerlach, 2019. "Semi-parametric Realized Nonlinear Conditional Autoregressive Expectile and Expected Shortfall," Papers 1906.09961, arXiv.org.
    11. Xiaochun Liu, 2016. "Markov switching quantile autoregression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 356-395, November.
    12. Richard Gerlach & Chao Wang, 2016. "Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Realized Measures," Papers 1612.08488, arXiv.org.
    13. Laura Garcia-Jorcano & Lidia Sanchis-Marco, 2023. "Measuring Systemic Risk Using Multivariate Quantile-Located ES Models," Journal of Financial Econometrics, Oxford University Press, vol. 21(1), pages 1-72.
    14. Kim, Minjo & Lee, Sangyeol, 2016. "Nonlinear expectile regression with application to Value-at-Risk and expected shortfall estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 1-19.
    15. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    16. Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel R. Smith, 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 150-160, January.
    17. Bonaccolto, Giovanni & Caporin, Massimiliano & Maillet, Bertrand B., 2022. "Dynamic large financial networks via conditional expected shortfalls," European Journal of Operational Research, Elsevier, vol. 298(1), pages 322-336.
    18. Yuta Kurose & Yasuhiro Omori, 2012. "Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline," CIRJE F-Series CIRJE-F-845, CIRJE, Faculty of Economics, University of Tokyo.
    19. Storti, Giuseppe & Wang, Chao, 2022. "Nonparametric expected shortfall forecasting incorporating weighted quantiles," International Journal of Forecasting, Elsevier, vol. 38(1), pages 224-239.
    20. Chen, Qian & Gerlach, Richard H., 2013. "The two-sided Weibull distribution and forecasting financial tail risk," International Journal of Forecasting, Elsevier, vol. 29(4), pages 527-540.

    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:spr:stmapp:v:30:y:2021:i:3:d:10.1007_s10260-020-00550-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.