Multivariate Risikomanagement

Abstract

In this thesis we propose a risk management methodology to high-dimensional financial portfolios. Instead of estimating the joint density of the portfolios in a high-dimensional space, we are encouraged by using the independent component analysis (ICA) to decompose the dependent risk factors to a linear transformation of independent components (ICs). The marginal density and the volatility process of each IC are estimated in a univariate dimension. Thereafter the joint densities and the dependence structures of the ICs and the original risk factors can be calculated using the statistical property of the independence and its linear transformation. We assume the marginal densities of ICs belong to the generalized hyperbolic (GH) distribution family since this family possesses semi-heavy tails and mimics the empirical distributions of the ICs appropriately. Further we implement a nonparametric adaptive methodology to estimate the local volatilities of ICs based on a homogeneity test. In order to check the reliability of the proposed methodology, we consider a portfolio in our study: a 2-dimensional exchange rates DEM/USD and GBP/USD with 4 different trading strategies. The empirical studies show that the performance of the VaR forecast using the proposed methodology is better than the popular Delta-Gamma-Normal model. All calculations and simulations are able to be recalculated with the software XploRe.