Conditional tail behaviour and Value at Risk

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