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On Computing Approximation of Correlations Using Bernstein Copula and Probabilistic Tools
Year Of Publication: 2011
Month Of Publication: May
Pages: 7
Download Count: 1
View Count: 1429
Comment Num: 0
Language: English
Source: working paper
Who Can Read: Free
Date: 8-20-2011
Publisher: Administrator
In this paper we restrict to approximations by Bernstein copula and follow the ideas of Sancetta and Satchell (2004) and Durrleman et al (2001). We give the approximation using elementary probabilistic tools as in Feller (1971) generalizing the work in Gzyl and Palacios (2003). Further, we establish that the empirical Bernstein copula converges uniformly to the true copula. We note that the measures of dependence, Kendall's Tau, Spearman's rank correlation, Hoe ding's dependence index and Pearson's coecient of mean square contingency can be approximated by those of approximating Bernstein copula and the empirical Bernstein copula. Based on the approximating (empirical) Bernstein copula, we give a numerical procedure to determine the VaR and ES. These approximations may be helpful as it is known that the biases in VaR estimates are due to the misspeci cation of the copula. Finally we compute nonparametric estimates of Kendall's tau and the Spearman's rank correlations between well known international indexes.
Mandrekar, V.S. Sign in to follow this author
Abegaz, Fentaw Sign in to follow this author
Naik-Nimbalkar, Uttara Sign in to follow this author
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