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

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 domi...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2008-04, Vol.42 (2), p.469-472
Main Authors: Fountain, Robert L., Herman, John R., Rustvold, D. Leif
Format: Article
Language:English
Subjects:
Copulas
Dependence measures
Distribution
Indexes
Insurance
Kendall distributions
Mathematical finance
Mathematics
Matrix algebra
Random variables
Stochastic models
Stochastic processes
Studies
Volatility
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Summary: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2006.11.007