Mathematical modeling of credit and equity risk beyond homogeneity and stationarity assumptions: statistical factor models and high-performance data mining

Analysis and prediction of financial risks, such as market and credit risks, is one of the central problems in modern economy. The task of adequate mathematical description of the available risk data in its very complex nature (resulting from the presence of different temporal and spatial, i.e. regional, sectorial and global, scales) becomes more and more important in the context of the recent evolutions of the world economy. Important questions thereby are: (i) an investigation of the mutual influence of different risks and their spatial (e.g., regional) and temporal (e.g., associated with the business cycle) evolution, (ii) identification of the most important impact factors that play a role in their dynamics.
Accumulation of sufficiently detailed economic time series has led to the creation of huge databases, implicitly containing hidden information that may enhance our understanding of the complex processes underlying the economy. However, the extraction of this essential information is hindered by the  non-stationary (in time) and non-homogeneous (geographically) nature of the analyzed data. Non-stationarity is understood here as the change over time of some model parameters, while non-homogeneity refers to the inherently different dynamics across statistical units (e.g., assets, corporations). Main problems arising from these issues most prominently manifest themselves in the following areas : (i) in the applicability of standard statistical methodology; (ii) in adequateness of the standard mathematical description of the underlying processes and (iii) in the practical computational implementation of the data analysis algorithms on modern supercomputer architectures.

The main aim of this project will be to address these problems in a specific context of credit and market risk analysis and modeling. It is planned to develop new methods of time series analysis for parameterizing the risks as a spatially coupled non-stationary and non-homogeneous stochastic process under the influence of global and local impact factors (e.g., gross national product, level of depth, stock market indicators, etc.). Conceptual development of new mathematical models and statistical analysis methods for market and credit risks will go hand-in-hand with implementation and comparison on high-performance platforms at the Swiss National Supercomputing Center (CSCS) in Lugano, Switzerland. Resulting methods and algorithms should be applied to transparent analysis of the available financial data bases for identification of statistically significant regional and global inter-dependencies and extraction of the significant external factors influencing Swiss economy.

This project bundles the expertise of the three PIs in non-stationary time series analysis (I. Horenko), financial econometrics/computational finance (P. Gagliardini, I. Horenko), credit risk models (P. Gagliardini) and high-performance architectures and algorithms (W. Sawyer).