Extreme value theory with application to financial data

Specialeforsvar: Rebecca Sandby Lindegaard

TItel: Extreme value theory with application to financial data

Abstract: This thesis investigates data from the financial market using extreme value theory in one and two dimensions, as well as explores extremal dependence and the clustering phenomenon, often observed in financial data. The thesis aims to use the theory and tools developed in extreme value theory, on data consisting of daily closing log-returns for the German multinational insurance and financial services company Allianz, as well as the French financial and insurance corporation AXA. An analysis of the heavy-tailed behavior of the Allianz log-returns is conducted, and later compared to the AXA log-returns, using one- dimensional extreme value theory, under the assumption of data being identically and independently distributed. Multidimensional extreme value theory and tools are introduced and used in an analysis of general dependence and extreme dependence both within, and between, the two closing logreturn series for Allianz and AXA. The analysis gives insight into the behavior, volatility and interdependence between, especially the extreme values, within the two chosen log-return series.
This can be useful when assessing the risks associated with investing in these stocks. This analysis is assessed and evaluated using stationary bootstrapping and simulations from a stochastic volatility model. Ultimately the analysis reveals significant dependence between the two log-return series, especially through the pattern that when extreme values occur on the same day, these tend to have the same sign. This means the extreme fluctuations follow each other in gains and losses and the risk associated with investing in the two stocks are similar.

Vejleder: Thomas Mikosch
Censor:   Mette Havning