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A non-parametric and entropy based analysis of the relationship between the VIX and S&P500

  • D.E. Allen

    ()

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

  • A. Kramadibrata

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam.)

  • R. Powell

    ()

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

  • A. K. Singh

    (School of Accounting Finance and Economics Edith Cowan University Joondalup Drive Joondalup Western Australia 6027)

This paper features an analysis of the relationship between the S&P500 Index and the VIX using daily data obtained from both the CBOE website and SIRCA (The Securities Industry Research Centre of the Asia Pacic). We explore the relationship between the S&P500 daily continuously compounded return series and a similar series for the VIX in terms of a long sample drawn from the CBOE running from 1990 to mid 2011 and a set of returns from SIRCA's TRTH datasets running from March 2005 to-date. We divide this shorter sample, which captures the behaviour of the new VIX, introduced in 2003, into four roughly equivalent sub-samples which permit the exploration of the impact of the Global Financial Crisis. We apply to our data sets a series of non-parametric based tests utilising entropy based metrics. These suggest that the PDFs and CDFs of these two return distributions change shape in various subsample periods. The entropy and MI statistics suggest that the degree of uncertainty attached to these distributions changes through time and using the S&P500 return as the dependent variable, that the amount of information obtained from the VIX also changes with time and reaches a relative maximum in the most recent period from 2011 to 2012. The entropy based non-parametric tests of the equivalence of the two distributions and their symmetry all strongly reject their respective nulls. The results suggest that parametric techniques do not adequately capture the complexities displayed in the behaviour of these series. This has practical implications for hedging utilising derivatives written on the VIX, which will be the focus of a subsequent study.

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File URL: http://eprints.ucm.es/16222/1/1219.pdf
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Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico in its series Documentos de Trabajo del ICAE with number 2012-19.

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Length: 19 pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:ucm:doicae:1219
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  1. Chatayan Wiphatthanananthakul & Michael McAleer, 2009. "Simple Expected Volatility (SEV) Index: Application to SET50 Index Options," CARF F-Series CARF-F-173, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  2. Isao Ishida & Michael McAleer & Kosuke Oya, 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX," KIER Working Papers 759, Kyoto University, Institute of Economic Research.
  3. Maasoumi, Esfandiar & Racine, Jeff, 2002. "Entropy and predictability of stock market returns," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 291-312, March.
  4. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Amaral, Teodosio Perez, 2013. "The rise and fall of S&P500 variance futures," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 151-167.
  5. Ebrahimi, Nader & Maasoumi, Esfandiar & Soofi, Ehsan S., 1999. "Ordering univariate distributions by entropy and variance," Journal of Econometrics, Elsevier, vol. 90(2), pages 317-336, June.
  6. Massimiliano Caporin & Michael McAleer, 2010. "Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models," Working Papers in Economics 10/06, University of Canterbury, Department of Economics and Finance.
  7. Brenner, Menachem & Ou, Ernest Y. & Zhang, Jin E., 2006. "Hedging volatility risk," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 811-821, March.
  8. Golan, Amos, 2002. "Information and Entropy Econometrics--Editor's View," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 1-15, March.
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  10. Steve Pincus, 2008. "Approximate Entropy as an Irregularity Measure for Financial Data," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 329-362.
  11. Anil Bera & Sung Park, 2008. "Optimal Portfolio Diversification Using the Maximum Entropy Principle," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 484-512.
  12. Tristen Hayfield & Jeffrey S. Racine, . "Nonparametric Econometrics: The np Package," Journal of Statistical Software, American Statistical Association, vol. 27(i05).
  13. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, 09.
  14. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
  15. Ishida, I. & McAleer, M.J. & Oya, K., 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 VIX," Econometric Institute Research Papers EI 2011-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  16. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  17. Amos Golan & Esfandiar Maasoumi, 2008. "Information Theoretic and Entropy Methods: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 317-328.
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