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

Author

Listed:
  • D.E. Allen

    (School of Accounting, Finance and Economics, Edith Cowan University)

  • A. Kramadibrata

    (School of Accounting, Finance and Economics, Edith Cowan University)

  • M. McAleer

    (Erasmus University Rotterdam)

  • R. Powell

    (School of Accounting, Finance and Economics, Edith Cowan University)

  • A. K. Singh

    (School of Accounting, Finance and Economics, Edith Cowan University)

Abstract

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 Pacific). 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.

Suggested Citation

  • D.E. Allen & A. Kramadibrata & M. McAleer & R. Powell & A. K. Singh, 2012. "A non-parametric and entropy based analysis of the relationship between the VIX and S&P500," KIER Working Papers 827, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:827
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    S&P500; VIX; Entropy; Non-Parametric Estimation; Quantile Regressions;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • E - Macroeconomics and Monetary Economics
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • G - Financial Economics

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