J. Risk Financial Manag. 2013, 6(1), 6-30; doi:10.3390/jrfm6010006
Article

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

Received: 3 October 2013; in revised form: 7 October 2013 / Accepted: 8 October 2013 / Published: 21 October 2013
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: This paper features an analysis of the relationship between the S&P 500 Index and the VIX using daily data obtained from the CBOE website and SIRCA (The Securities Industry Research Centre of the Asia Pacific). We explore the relationship between the S&P 500 daily return series and a similar series for the VIX in terms of a long sample drawn from the CBOE from 1990 to mid 2011 and a set of returns from SIRCA’s TRTH datasets from March 2005 to-date. This shorter sample, which captures the behavior of the new VIX, introduced in 2003, is divided into four sub-samples which permit the exploration of the impact of the Global Financial Crisis. We apply a series of non-parametric based tests utilizing 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 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 behavior of these series. This has practical implications for hedging utilizing derivatives written on the VIX.
Keywords: S&P 500; VIX; entropy; non-parametric estimation; quantile regressions
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MDPI and ACS Style

Allen, D.E.; McAleer, M.; Powell, R.; Singh, A.K. A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500. J. Risk Financial Manag. 2013, 6, 6-30.

AMA Style

Allen DE, McAleer M, Powell R, Singh AK. A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500. Journal of Risk and Financial Management. 2013; 6(1):6-30.

Chicago/Turabian Style

Allen, David E.; McAleer, Michael; Powell, Robert; Singh, Abhay K. 2013. "A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500." J. Risk Financial Manag. 6, no. 1: 6-30.

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