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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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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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description	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.
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source	International Bibliography of the Social Sciences (IBSS); Backfile Package - Economics, Econometrics and Finance (Legacy) [YET]; Elsevier; Backfile Package - Mathematics (Legacy) [YMT]
subjects	Copulas Dependence measures Distribution Indexes Insurance Kendall distributions Mathematical finance Mathematics Matrix algebra Random variables Stochastic models Stochastic processes Studies Volatility
title	An application of Kendall distributions and alternative dependence measures: SPX vs. VIX
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