Tail dependence in financial data

Abstract

In this thesis we model extreme log-returns on economic variables and apply this to Ortec Finance's model. These extreme log-returns are relevant for risk management applications such as Value-at-Risk and other measures of tail risk. We use extreme value theory to simulate economic variables with the desired tail behaviour. We pay special attention to correlations between economic variables, since these tend to increase during financial crises. This suggest the possibility of tail dependence and we use copula theory to model behaviour similarly to what we observed historically.

We find that a single parameter, the tail index, can be used to model the tail behaviour of an economic variable. To model the tail dependence between economic variables we can also use a single parameter namely the tail dependence coefficient. We model the complete dependence structure with a semiparametric copula, such that the copula has the desired tail dependence coefficient, but also approximates the dependence outside the tails.

These techniques are applied in the context of vector autoregressive models, since these models are used to describe the statistical factors in Ortec Finance's Dynamic Scenario Generator, which generates future economic scenarios. We provide a first stylized indication on how these techniques could be applied in the context of Ortec Finance's model.