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

Allen, David E. and Kramadibrata, A. and McAleer, Michael and Powell, R. and Singh, A. K. (2012) A non-parametric and entropy based analysis of the relationship between the VIX and S&P500. [Working Paper or Technical Report] (Unpublished)

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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 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.

Item Type:Working Paper or Technical Report
Additional Information:Preprint submitted to Elsevier
Uncontrolled Keywords:S&P500, VIX, Entropy, Non-Parametric Estimation, Quantile Regressions.
Subjects:Social sciences > Economics > Econometrics
Series Name:UNSPECIFIED
Volume:2012
Number:19
ID Code:16222
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Deposited On:04 Sep 2012 12:47
Last Modified:15 Nov 2013 10:49

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