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Conditional tail behaviour and Value at Risk 

Authors: Fabio Bellini a; Gianna Figagrave-talamanca b
Affiliations:   a University of Milano-Bicocca, Piazza Ateneo Nuovo 1, 20126 Milan, Italy
b University of Perugia, via Pascoli 20, 06123 Perugia, Italy
DOI: 10.1080/14697680601155516
Publication Frequency: 10 issues per year
Published in: journal Quantitative Finance, Volume 7, Issue 6 December 2007 , pages 599 - 607
Formats available: HTML (English) : PDF (English)
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Abstract

In this paper we study the tail behaviour of eight major market indexes stratifying data according to the violation of a high threshold on the previous day. The distributional differences found can be exploited to improve VaR calculations in several settings, giving rise to what we call 'MCVaR'. We compare the performance of MCVaR with unconditioned VaR calculation methods and with GARCH VaR by means of several back-testing techniques that take into account not only the number of violations but also their magnitude and clustering.
Keywords: Value at Risk; Paretian tails; GARCH; Runs test; Back testing
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