Applications of Kernel Methods in Financial Risk Management

Since their introduction Kernel Methods have proven their superior performance in many different application areas. Recently these algorithms have also been employed for different tasks in the area of finance. In this contribution we present an introduction to the methodology and give an overview of successful applications in finance. Subsequently two promising areas for the use of these advanced statistical learning methods are introduced, namely integrated risk management and parameter estimation in the Basel II capital accord context. Integrated risk management is concerned with the simultaneous consideration of the major sources of risk and return for today’s financial institutions. While risk measurement is typically still performed using isolated and substantially different quantitative models per risk category, we describe a novel approach based on Support Vector Machines (SVMs). Through training the SVM learns the implicit relation between different risk types. The Loss Given Default (LGD) represents a parameter to be estimated by banks when using internal rating based approaches within their Basel II implementation. Real-world applications indicate that linear relations between the input values may fail to describe the parameter output. We have used SVMs with varying kernels and obtained rather reliable estimates for the LGD compared to standard methods