Essays on univariate and multivariate modeling of financial market risks

Abstract

This dissertation explores risk management with regard to the univariate and multivariate modeling of financial market risks by applying three different scientific research methods: the deductive approach, the design and implementation of a model as well as the inductive analysis of simulation results. The introduction in chapter one is followed by a theory-based approach in the second chapter with the objective to investigate implications of mean reversion in asset prices with respect to the optimal hedging strategy in an expected utility framework. Chapters three and four are motivated by the growing criticism of elliptical models in risk management and focus on improvements of dynamic vine copula models. Both chapters start with the presentation of a modified model approach, continue with its implementation in an experimental framework, and conclude with an inductive analysis of the simulation results. The third chapter deals with smooth nonparametric Bernstein vine copula models which are shown to be a crucial extension in terms of reducing model risk and also well suited for the task of approximating the true dependence structure of multivariate data sets. The follow-up study presented in chapter four deals with the so-called mixture pair-copula-constructions. The models accuracy is demonstrated by performing both a simulation and an empirical study on the in-sample and out-of-sample Value-at-Risk forecasting. Moreover the modeling approach helps risk managers to save on regulatory risk capital. The final chapter five pushes forward into a new area of research relating to financial markets. A statistical modeling framework for specifying, estimating, and testing time series of investor attention measured by Google Search Data is provided. Empirical evidence of strong non-linear and asymmetric dependence in the attention investors give to companies is documented. Furthermore, the existence of extreme dependence between stock returns and the corresponding Google Search Data is shown. Finally, a striking similarity in the joint distributions of a multivariate bank stock portfolio and the corresponding portfolio of Google Search Data is presented.