IDEAS home Printed from https://ideas.repec.org/p/cbt/econwp/09-15.html
   My bibliography  Save this paper

Bayesian Extreme Value Mixture Modelling for Estimating VaR

Author

Listed:

Abstract

A new extreme value mixture modelling approach for estimating Value-at-Risk (VaR) is proposed, overcoming the key issues of determining the threshold which defines the distribution tail and accounts for uncertainty due to threshold choice. A two-stage approach is adopted: volatility estimation followed by conditional extremal modelling of the independent innovations. Bayesian inference is used to account for all uncertainties and enables inclusion of expert prior information, potentially overcoming the inherent sparsity of extremal data. Simulations show the reliability and flexibility of the proposed mixture model, followed by VaR forecasting for capturing returns during the current financial crisis.

Suggested Citation

  • Xin Zhao & Carl John Scarrott & Marco Reale & Les Oxley, 2009. "Bayesian Extreme Value Mixture Modelling for Estimating VaR," Working Papers in Economics 09/15, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:09/15
    as

    Download full text from publisher

    File URL: https://repec.canterbury.ac.nz/cbt/econwp/0915.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    2. Les Oxley & Marco Reale & Carl Scarrott & Xin Zhao, 2009. "Extreme Value GARCH modelling with Bayesian Inference," Working Papers in Economics 09/05, University of Canterbury, Department of Economics and Finance.
    3. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    4. 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.
    5. 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.
    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. Shcherba, Alexandr, 2012. "Market risk valuation modeling for the European countries at the financial crisis of 2008," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 27(3), pages 20-35.
    2. C J Scarrott & A MacDonald, 2010. "Extreme-value-model-based risk assessment for nuclear reactors," Journal of Risk and Reliability, , vol. 224(4), pages 239-252, December.

    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. Zhao, Xin & Scarrott, Carl John & Oxley, Les & Reale, Marco, 2011. "GARCH dependence in extreme value models with Bayesian inference," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1430-1440.
    2. Xin Zhao & Carl Scarrott & Les Oxley & Marco Reale, 2010. "Extreme value modelling for forecasting market crisis impacts," Applied Financial Economics, Taylor & Francis Journals, vol. 20(1-2), pages 63-72.
    3. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    4. Oliver Linton & Dajing Shang & Yang Yan, 2012. "Efficient estimation of conditional risk measures in a semiparametric GARCH model," CeMMAP working papers CWP25/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Zhao, Zifeng & Zhang, Zhengjun & Chen, Rong, 2018. "Modeling maxima with autoregressive conditional Fréchet model," Journal of Econometrics, Elsevier, vol. 207(2), pages 325-351.
    6. Pushpa Dissanayake & Teresa Flock & Johanna Meier & Philipp Sibbertsen, 2021. "Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights," Mathematics, MDPI, vol. 9(21), pages 1-33, November.
    7. 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.
    8. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Documents de travail du Centre d'Economie de la Sorbonne 16034rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2017.
    9. Tomohiro Ando & Matthew Greenwood-Nimmo & Yongcheol Shin, 2022. "Quantile Connectedness: Modeling Tail Behavior in the Topology of Financial Networks," Management Science, INFORMS, vol. 68(4), pages 2401-2431, April.
    10. 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.
    11. 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.
    12. Timo Dimitriadis & Yannick Hoga, 2022. "Dynamic CoVaR Modeling and Estimation," Papers 2206.14275, arXiv.org, revised Jan 2025.
    13. 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.
    14. 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.
    15. Anna Kiriliouk & Chen Zhou, 2024. "Tail Risk Analysis for Financial Time Series," Papers 2409.18643, arXiv.org.
    16. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Value-at-risk methodologies for effective energy portfolio risk management," Economic Analysis and Policy, Elsevier, vol. 62(C), pages 197-212.
    17. 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.
    18. 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.
    19. 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.
    20. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.

    More about this item

    Keywords

    Extreme values; Bayesian; Threshold estimation; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    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:cbt:econwp:09/15. 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: Albert Yee (email available below). General contact details of provider: https://edirc.repec.org/data/decannz.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.