Skip to main content
SpringerLink
Log in

Dynamic bivariate normal copula

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

Normal copula with a correlation coefficient between −1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, Hüsler and Reiss (1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by Hüsler and Reiss (1989). A simulation study and real data analysis are presented too.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Benth F E, Kettler P C. Dynamic copula models for the spark spread. Quant Finance, 2011, 11: 407–421

    Article  MathSciNet  Google Scholar 

  2. Channouf N, L’Ecuyer P. A normal copula model for the arrival process in a call center. Int Trans Oper Res, 2012, 19: 771–787

    Article  MathSciNet  MATH  Google Scholar 

  3. Fan J, Gijbels I. Local Polynomial Modelling and Its Applications. New York: Chapman & Hall, 1996

    MATH  Google Scholar 

  4. Frick M, Reiss R-D. Expansions and penultimate distributions of maxima of bivariate normal random vectors. Statist Probab Lett, 2013, 83: 2563–2568

    Article  MathSciNet  MATH  Google Scholar 

  5. Fung T, Seneta E. The bivariate normal copula function is regularly varying. Statist probab Lett, 2011, 81: 1670–1676

    Article  MathSciNet  MATH  Google Scholar 

  6. Guégan D, Zhang J. Change analysis of a dynamic copula for measuring dependence in multivariate financial data. Quant Finance, 2010, 10: 421–430

    Article  MathSciNet  MATH  Google Scholar 

  7. Hall P, Heyde C C. Martingale Limit Theory and Its Application. New York: Academic Press, 1980

    MATH  Google Scholar 

  8. Hashorva E. Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution. Statist Probab Lett, 2005, 72: 125–135

    Article  MathSciNet  MATH  Google Scholar 

  9. Hashorva E. On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays. Statist Probab Lett, 2006, 76: 2027–2035

    Article  MathSciNet  MATH  Google Scholar 

  10. Hüsler J, Reiss R-D. Maxima of normal random vectors: between independence and complete dependence. Statist Probab Lett, 1989, 7: 283–286

    Article  MathSciNet  MATH  Google Scholar 

  11. Klaassen C A J, Wellner J A. Efficient estimation in the bivariate normal copula model: Normal margins are least favourable. Bernoulli, 1997, 3: 55–77

    Article  MathSciNet  MATH  Google Scholar 

  12. McNeil A J, Frey R, Embrechts P. Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton: Princeton University Press, 2005

    MATH  Google Scholar 

  13. Mendes B V M, de Melo E F L. Local estimation of dynamic copula models. Int J Theor Appl Finance, 2010, 13: 241–258

    Article  MathSciNet  MATH  Google Scholar 

  14. Meyer C. The bivariate normal copula. Commun Stat Theory Methods, 2013, 42: 2402–2422

    Article  MathSciNet  MATH  Google Scholar 

  15. Plackett R L. A reduction formula for normal multivariate integrals. Biometrika, 1954, 41: 351–360

    Article  MathSciNet  MATH  Google Scholar 

  16. Sibuya M. Bivariate extreme statistics. Ann Inst Statist Math, 1960, 11: 195–210

    Article  MathSciNet  MATH  Google Scholar 

  17. Shorack G R, Wellner J A. Empirical Processes With Applications To Statistics. New York: John Wiley & Sons, 1986

    MATH  Google Scholar 

  18. Van den Goorbergh R W J, Genest C, Werker B J M. Bivariate option pricing using dynamic copula models. Insurance Math Econom, 2005, 37: 101–114

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Xin Liao & ZuoXiang Peng

  2. Department of Risk Management and Insurance, Georgia State University, Atlanta, GA, 30303, USA

    Liang Peng

  3. Department of Finance, Beijing Technology and Business University, Beijing, 100048, China

    YanTing Zheng

Authors
  1. Xin Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. ZuoXiang Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. YanTing Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ZuoXiang Peng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liao, X., Peng, L., Peng, Z. et al. Dynamic bivariate normal copula. Sci. China Math. 59, 955–976 (2016). https://doi.org/10.1007/s11425-015-5114-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-015-5114-1

Keywords

MSC(2010)

Search

Navigation