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.*
[
nº 19,
2012,
]
(Unpublished)

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Available under License Creative Commons Attribution Non-commercial. 3MB |

Official URL: http://eprints.ucm.es/16222/

## 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: | |

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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