IDEAS home Printed from https://ideas.repec.org/p/cbt/econwp/09-05.html
   My bibliography  Save this paper

Extreme Value GARCH modelling with Bayesian Inference

Author

Listed:

Abstract

Extreme value theory is widely used financial applications such as risk analysis, forecasting and pricing models. One of the major difficulties in the applications to finance and economics is that the assumption of independence of time series observations is generally not satisfied, so that the dependent extremes may not necessarily be in the domain of attraction of the classical generalised extreme value distribution. This study examines a conditional extreme value distribution with the added specification that the extreme values (maxima or minima) follows a conditional autoregressive heteroscedasticity process. The dependence has been modelled by allowing the location and scale parameters of the extreme distribution to vary with time. The resulting combined model, GEV-GARCH, is developed by implementing the GARCH volatility mechanism in these extreme value model parameters. Bayesian inference is used for the estimation of parameters and posterior inference is available through the Markov Chain Monte Carlo (MCMC) method. The model is firstly applied to relevant simulated data to verify model stability and reliability of the parameter estimation method. Then real stock returns are used to consider evidence for the appropriate application of the model. A comparison is made between the GEV-GARCH and traditional GARCH models. Both the GEV-GARCH and GARCH show similarity in the resulting conditional volatility estimates, however the GEV-GARCH model differs from GARCH in that it can capture and explain extreme quantiles better than the GARCH model because of more reliable extrapolation of the tail behaviour.

Suggested Citation

  • 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.
    • Handle: RePEc:cbt:econwp:09/05
    as

    Download full text from publisher

    File URL: https://repec.canterbury.ac.nz/cbt/econwp/0905.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Scharth, Marcel & Medeiros, Marcelo C., 2009. "Asymmetric effects and long memory in the volatility of Dow Jones stocks," International Journal of Forecasting, Elsevier, vol. 25(2), pages 304-327.
    2. 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.
    3. 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.
    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. 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.
    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.

    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, Zifeng & Zhang, Zhengjun & Chen, Rong, 2018. "Modeling maxima with autoregressive conditional Fréchet model," Journal of Econometrics, Elsevier, vol. 207(2), pages 325-351.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Turan G. Bali, 2007. "A Generalized Extreme Value Approach to Financial Risk Measurement," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1613-1649, October.
    11. Krzysztof Echaust & Małgorzata Just, 2021. "Tail Dependence between Crude Oil Volatility Index and WTI Oil Price Movements during the COVID-19 Pandemic," Energies, MDPI, vol. 14(14), pages 1-21, July.
    12. 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.
    13. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
    14. Halkos, George & Tsirivis, Apostolos, 2019. "Using Value-at-Risk for effective energy portfolio risk management," MPRA Paper 91674, University Library of Munich, Germany.
    15. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    16. Chen, Ray-Bing & Chen, Ying & Härdle, Wolfgang K., 2014. "TVICA—Time varying independent component analysis and its application to financial data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 95-109.
    17. Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2015. "Testing for structural breaks in correlations: Does it improve Value-at-Risk forecasting?," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 135-152.
    18. Härdle, Wolfgang Karl & Hautsch, Nikolaus & Pigorsch, Uta, 2008. "Measuring and modeling risk using high-frequency data," SFB 649 Discussion Papers 2008-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    19. Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
    20. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.

    More about this item

    Keywords

    Extreme value distribution; dependency; Bayesian; MCMC; Return quantile;
    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:09/05. 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.