Focus Credit Risk and Statistics

Fraunhofer ITWM

Credit derivatives got lately a bad reputation as too complex instruments and too difficult to understand. A precise mathematical evaluation of these products can help and bring clarity and objectivity in the given debate: These products will still be needed for an efficient and simple risk transfer used in risk management, portfolio optimization and for long-term investments.

The ITWM has lots of experience this area and since 2004 implemented various models in evaluation tools for banks and asset managers, usually in the form of Excel sheets, how they are used on trading floors, linked to C++-, C#- or Matlab-libraries.

The Department of Financial Mathematics is also involved in the research in this area, in particular with papers about the optimal leverage for CPDOs and a Markov model for CDOs.


To understand these instruments the statistical analysis and modeling is more important than elsewhere in the financial mathematics: The world of financial products is too complex to be captured by simple models. What models should we use then? What about the data quality and completeness?

In this regard we pursue three strategies:

  • First, financial statistics, particularly in the field of time series analysis, offers a wide range of models to depict this reality. We work for example with Hidden Markov models which allow, because of possible regime changes, a flexible model-building of moderate complexity. Financial time series from different areas such as commodities, stock prices or indices can be modeled realistically and predictions taking into account possible changes in the state of the financial market can be made.

    Our research focuses on filtering methods for Hidden Markov models.
  • Second, robust statistics provides the general strategy in dealing with model uncertainty: Unfortunately most known methods of statistics are precisely adjusted to the underlying model but fail after just a few outliers or small deviations from the model. Robust statistics provides techniques that (a) quantify the influence of a single observation at the level of the target value (risk measure, predicted stock price) and (b) present outlier-robust alternatives to the traditional methods that restrict the influence of single observations on the target value.

    We are actively involved in the research on robustification of the Kalman filter and the EM algorithm for parameter estimation.
  • Third, the analysis of the data quality in terms of outliers, fractures and missing values: What to do if certain information is missing in the data? How do we deal with data in which there are jumps (e.g. a stock split) and how do we handle weekend and holiday effects?

    Here we have expertise in modern imputations techniques allowing to use the information in this incomplete data efficiently.

 

Our statistical analysis also includes the application development of new statistical models for specific customer needs in pricing in illiquid markets, the valuation of loans and risk management.

In risk management we can create custom-built models for quantifying risk, which depict the situation of each company better than the classic approaches and thus lead to better adjusted and often lower capital requirements (Basel II Framework) for the company. This applies particularly to operational risks and liquidity risks.

A particular focus is on extreme events that occur only with a small probability but have a strong impact on losses. To this end our department develops optimal-robust measures for risk quantification.

Selected Projects

Tools

  • Idea: a robust Quantil-Calculator

References and Partners