IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v47y2010i1p13-20.html
   My bibliography  Save this article

Estimating generalized state density of near-extreme events and its applications in analyzing stock data

Author

Listed:
  • Lin, Jin-Guan
  • Huang, Chao
  • Zhuang, Qing-Yun
  • Zhu, Li-Ping

Abstract

This paper studies the generalized state density (GDOS) of near-historical extreme events of a set of independent and identically distributed (i.i.d.) random variables. The generalized density of states is proposed which is defined as a probability density function (p.d.f.). For the underlying distribution in the domain of attraction of the three well-known extreme value distribution families, we show the approximate form of the mean GDOS. Estimates of the mean GDOS are presented when the underlying distribution is unknown and the sample size is sufficiently large. Some simulations have been performed, which are found to agree with the theoretical results. The closing price data of the Dow-Jones industrial index are used to illustrate the obtained results.

Suggested Citation

  • Lin, Jin-Guan & Huang, Chao & Zhuang, Qing-Yun & Zhu, Li-Ping, 2010. "Estimating generalized state density of near-extreme events and its applications in analyzing stock data," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 13-20, August.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:1:p:13-20
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(10)00032-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    2. Brands, J. J. A. M. & Steutel, F. W. & Wilms, R. J. G., 1994. "On the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 209-217, June.
    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. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Papers 1106.0039, arXiv.org.
    2. Chao Huang & Jin-Guan Lin, 2014. "Modified maximum spacings method for generalized extreme value distribution and applications in real data analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 867-894, October.
    3. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Post-Print hal-00827942, HAL.
    4. Chao Huang & Jin-Guan Lin & Yan-Yan Ren, 2013. "Testing for the shape parameter of generalized extreme value distribution based on the $$L_q$$ -likelihood ratio statistic," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 641-671, July.
    5. Politi, Mauro & Millot, Nicolas & Chakraborti, Anirban, 2012. "The near-extreme density of intraday log-returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 147-155.
    6. Wang, Hai-Kun & Li, Yan-Feng & Huang, Hong-Zhong & Jin, Tongdan, 2017. "Near-extreme system condition and near-extreme remaining useful time for a group of products," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 103-110.

    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. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    2. Dimitrakopoulos, Dimitris N. & Kavussanos, Manolis G. & Spyrou, Spyros I., 2010. "Value at risk models for volatile emerging markets equity portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(4), pages 515-526, November.
    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. Fong Chan, Kam & Gray, Philip, 2006. "Using extreme value theory to measure value-at-risk for daily electricity spot prices," International Journal of Forecasting, Elsevier, vol. 22(2), pages 283-300.
    5. Bi, Guang & Giles, David E., 2009. "Modelling the financial risk associated with U.S. movie box office earnings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2759-2766.
    6. Karmakar, Madhusudan & Paul, Samit, 2016. "Intraday risk management in International stock markets: A conditional EVT approach," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 34-55.
    7. Karmakar, Madhusudan & Shukla, Girja K., 2015. "Managing extreme risk in some major stock markets: An extreme value approach," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 1-25.
    8. Cifter, Atilla, 2011. "Value-at-risk estimation with wavelet-based extreme value theory: Evidence from emerging markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2356-2367.
    9. Vêlayoudom Marimoutou & Bechir Raggad & Abdelwahed Trabelsi, 2006. "Extreme Value Theory and Value at Risk : Application to Oil Market," Working Papers halshs-00410746, HAL.
    10. Ozun, Alper & Cifter, Atilla & Yilmazer, Sait, 2007. "Filtered Extreme Value Theory for Value-At-Risk Estimation," MPRA Paper 3302, University Library of Munich, Germany.
    11. Marimoutou, Velayoudoum & Raggad, Bechir & Trabelsi, Abdelwahed, 2009. "Extreme Value Theory and Value at Risk: Application to oil market," Energy Economics, Elsevier, vol. 31(4), pages 519-530, July.
    12. Saša ŽIKOVIÆ & Randall K. FILER, 2013. "Ranking of VaR and ES Models: Performance in Developed and Emerging Markets," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(4), pages 327-359, August.
    13. Singh, Abhay K. & Allen, David E. & Robert, Powell J., 2013. "Extreme market risk and extreme value theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 310-328.
    14. 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.
    15. Jose Oliver Q. Suaiso & Dennis S. Mapa, 2009. "Measuring market risk using extreme value theory," Philippine Review of Economics, University of the Philippines School of Economics and Philippine Economic Society, vol. 46(2), pages 91-121, December.
    16. Zuoxiang, Peng & Miaomiao, Liu & Nadarajah, Saralees, 2010. "Asymptotic expansions for the location invariant moment-type estimator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 982-998.
    17. Sasa Zikovic & Randall Filer, 2009. "Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets," CESifo Working Paper Series 2820, CESifo.
    18. Imed Gammoudi & Lotfi BelKacem & Mohamed El Ghourabi, 2014. "Value at Risk Estimation for Heavy Tailed Distributions," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 8(3), pages 109-125.
    19. 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.
    20. 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.

    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:eee:insuma:v:47:y:2010:i:1:p:13-20. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.