IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

A non-parametric and entropy based analysis of the relationship between the VIX and S&P 500

  • David E Allen

    ()

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

  • Michael McAleer

    (Erasmus School of Economics, Erasmus University Rotterdam)

  • Robert Powell

    ()

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

  • Abhay Kumar Singh

    ()

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

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 Pacifc). 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.ecu.edu.au/__data/assets/pdf_file/0006/441555/Wp1302da.pdf
File Function: Full text
Download Restriction: no

Paper provided by Edith Cowan University, School of Business in its series Working papers with number 2013-01.

as
in new window

Length: 19 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:ecu:wpaper:2013-01
Contact details of provider: Postal: 270 Joondalup Drive, Joondalup, Western Australia, 6027
Web page: http://www.ecu.edu.au/schools/business/overview

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  2. Chatayan Wiphatthanananthakul & Michael McAleer, 2009. "A Simple Expected Volatility (SEV) Index: Application to SET50 Index Options," CIRJE F-Series CIRJE-F-672, CIRJE, Faculty of Economics, University of Tokyo.
  3. 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," Managerial Finance, Emerald Group Publishing, vol. 37(11), pages 1048-1067, October.
  4. Massimiliano Caporin & Michael McAleer, 2010. "Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models," CIRJE F-Series CIRJE-F-713, CIRJE, Faculty of Economics, University of Tokyo.
  5. 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.
  6. 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.
  7. Brenner, Menachem & Ou, Ernest Y. & Zhang, Jin E., 2006. "Hedging volatility risk," Journal of Banking & Finance, Elsevier, vol. 30(3), pages 811-821, March.
  8. Chang, C-L. & Jimenez-Martin, J-A. & McAleer, M.J. & Perez-Amaral, T., 2011. "The Rise and Fall of S&P500 Variance Futures," Econometric Institute Research Papers EI2011-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  9. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(1), pages 1-88, March.
  10. Maasoumi, Esfandiar & Racine, Jeff, 2002. "Entropy and predictability of stock market returns," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 291-312, March.
  11. Tristen Hayfield & Jeffrey S. Racine, . "Nonparametric Econometrics: The np Package," Journal of Statistical Software, American Statistical Association, vol. 27(i05).
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ecu:wpaper:2013-01. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Web Business Team)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.