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A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500

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Author Info

  • David E. Allen

    (Edith Cowan University)

  • Michael McAleer

    (Erasmus University Rotterdam, Complutense University of Madrid, Spain, and Kyoto University, Japan)

  • Robert Powell

    (Edith Cowan University)

  • Abhay K. Singh

    (Edith Cowan University)

Abstract

This paper features an analysis of the relationship between the S&P 500 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&P 500 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&P 500 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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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 13-018/III.

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Date of creation: 17 Jan 2013
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Handle: RePEc:dgr:uvatin:20130018

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Web page: http://www.tinbergen.nl

Related research

Keywords: S&P 500; VIX; Entropy; Non-Parametric Estimation; Quantile Regressions;

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  1. 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.
  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," Working Papers in Economics 11/11, University of Canterbury, Department of Economics and Finance.
  3. McAleer, Michael & Wiphatthanananthakul, Chatayan, 2010. "A simple expected volatility (SEV) index: Application to SET50 index options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2079-2090.
  4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  5. Chia-Lin Chang & Juan-Ángel Jiménez-Martín & Michael McAleer & Teodosio Pérez Amaral, 2011. "The Rise and Fall of S&P500 Variance Futures," Working Papers in Economics 11/32, University of Canterbury, Department of Economics and Finance.
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  7. Massimiliano Caporin & Michael McAleer, 2010. "Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models," KIER Working Papers 738, Kyoto University, Institute of Economic Research.
  8. 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.
  9. Maasoumi, Esfandiar & Racine, Jeff, 2002. "Entropy and predictability of stock market returns," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 291-312, March.
  10. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
  11. Brenner, Menachem & Ou, Ernest Y. & Zhang, Jin E., 2006. "Hedging volatility risk," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 811-821, March.
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