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An application of Kendall distributions and alternative dependence measures: SPX vs. VIX

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  • Fountain, Robert L.
  • Herman Jr., John R.
  • Rustvold, D. Leif

Abstract

Most of the recently-defined notions of positive or negative dependence rely upon a variety of orderings of bivariate random vectors. These orderings are generally partial orders, and thus there are many pairs of random vectors which are not comparable. By using a weakened version of stochastic domination and the concepts of Kendall distributions and metacopulas, an entirely new class of orderings, in which the comparability issue is resolved, has been recently created. Each ordering in this class can be used to construct a measure of dependence. A detailed example will be given, using data from the Standard & Poor's 500 index and Chicago Board of Trades index for implied volatility.

Suggested Citation

  • Fountain, Robert L. & Herman Jr., John R. & Rustvold, D. Leif, 2008. "An application of Kendall distributions and alternative dependence measures: SPX vs. VIX," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 469-472, April.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:469-472
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    References listed on IDEAS

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    1. Khaledi, Baha-Eldin & Kochar, Subhash, 2005. "Dependence orderings for generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 357-367, July.
    2. Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "Stochastic Comparisons and Dependence among Concomitants of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 262-281, May.
    3. Boland, Philip J. & Hollander, Myles & Joag-Dev, Kumar & Kochar, Subhash, 1996. "Bivariate Dependence Properties of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 75-89, January.
    4. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2003. "Kendall distribution functions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 263-268, November.
    5. Avérous, Jean & Genest, Christian & C. Kochar, Subhash, 2005. "On the dependence structure of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 159-171, May.
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    Cited by:

    1. Saffet Akdağ & İlker Kiliç & Hakan Yildirim, 2019. "Does VIX scare stocks of tourism companies?," Letters in Spatial and Resource Sciences, Springer, vol. 12(3), pages 215-232, December.
    2. Liang, Ruibin & Cheng, Sheng & Cao, Yan & Li, Xinran, 2024. "Multi-scale impacts of oil shocks on travel and leisure stocks: A MODWT-Bayesian TVP model with shrinkage approach," Technological Forecasting and Social Change, Elsevier, vol. 200(C).

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