Multivariate Extreme value Analysis of Financial Data

Specialeforsvar ved Lasse Tino Jensen

Titel: Multicariate Extreme Value Analysis fo Financial Data

Abstract: In this thesis we will be exploring multivariate extreme value theory and how to use this theory to estimate the probability of rare events occurring. Multivariate extreme value theory is useful in environmental studies such as sea levels and wave heights leading to floods, and in insurance where large claims can lead to ruin. We will however be using  the theory to analyse the extremal behaviour of a multivariate financial time series consis-ting of the closing stock prices of Danske Bank and Nordea. We will be presenting a theory for examining the extremal dependence via the extremogram and cross-extremogram following the work of Davis & Mikosch [6] and Davis, Mikosch & Cribben [7], as well as the multivariate extreme value theory from de Haan & Ferreira [1] and de Haan & de Ronde [3], leading us to estimating the probabilities of rare events occurring within three different kinds of failure sets using the exponent measure. Here we will also be tackling the problem of estimating the probability of events which has not occurred yet, by scaling of the original failure set. 

Vejleder: Thomas Mikosch
Censor:   Mette M Havning