In financial and actuarial sciences, knowledge about the dependence structure is of a great importance. Unfortunately this kind of information is often scarce. Many research has already been done in this field e.g. through the theory of comonotonicity. It turned out that a comonotonic dependence structure provides a very useful tool when approximating an unknown but (preferably strongly) positive dependence structure. As a consequence of this evolution, there is a need for a measure which reflects how close a given dependence structure approaches the comonotonic one. In this contribution, we design a measure of (positive) association between n variables (X1,X2, • • • ,Xn) which is useful in this context. The proposed measure, the comonotonicity coefficient _(X) takes values in the range [0, 1]. As we want to quantify the degree of comonotonicity, _(X) is defined in such a way that it equals 1 in case (X1,X2, • • • ,Xn) is comonotonic and 0 in case (X1,X2, • • • ,Xn) is independent. It should be mentioned that both the marginal distributions and the dependence structure of the vector (X1,X2, • • • ,Xn) will have an effect on the resulting value of this comonotonicity coefficient. In a first part, we show how _(X) can be designed analytically, by making use of copulas for modeling the dependence structure. In the particular case where n = 2, we compare our measure with the classic dependence measures and find some remarkable relations between our measure and the Pearson and Spearman correlation coefficients. In a second part, we focus on the case of a discounting Gaussian process and we investigate the performance of our comonotonicity coefficient in such an environment. This provides us insight in the reason why the comonotonic structure is a good approximation for the dependence structure.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. 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.
Publisher Info
Paper provided by University of Antwerp, Faculty of Applied Economics in its series Working Papers with number
2006030.
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.: