Quantitative Validation: An Overview and Framework for PD Backtesting and Benchmarking.

The aim of credit risk models is to identify and quantify future outcomes of a set of risk measurements. In other words, the model's purpose is to provide as good an approximation as possible of what constitutes the true underlying risk relationship between a set of inputs and a target variable. These parameters are used for regulatory capital calculations to determine the capital needed that serves a buffer to protect depositors in adverse economic conditions. In order to manage model risk, financial institutions need to set up validation processes so as to monitor the quality of the models on an ongoing basis. Validation is important to inform all stakeholders (e.g. board of directors, senior management, regulators, investors, borrowers, …) and as such allow them to make better decisions. Validation can be considered from both a quantitative and qualitative point of view. Backtesting and benchmarking are key quantitative validation tools. In backtesting, the predicted risk measurements (PD, LGD, CCF) will be contrasted with observed measurements using a workbench of available test statistics to evaluate the calibration, discrimination and stability of the model. A timely detection of reduced performance is crucial since it directly impacts profitability and risk management strategies. The aim of benchmarking is to compare internal risk measurements with external risk measurements so to allow to better gauge the quality of the internal rating system. This paper will focus on the quantitative PD validation process within a Basel II context. We will set forth a traffic light indicator approach that employs all relevant statistical tests to quantitatively validate the used PD model, and document this complete approach with a reallife case-study.Framework; Benchmarking; Credit; Credit scoring; Control;

Ants Constructing Rule-Based Classifiers

Book series: Studies in Computational Intelligencestatus: publishe

Fractional dynamics of coupled oscillators with long-range interaction

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise interaction. The corresponding term in dynamical equations is proportional to $1/|n-m|^{\alpha+1}$. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order $\alpha$, when $0<\alpha<2$. We consider few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on $\alpha$. The presence of fractional derivative leads also to the occurrence of localized structures. Particular solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear Schrodinger) equation are derived. These solutions are interpreted as synchronized states and localized structures of the oscillatory medium.Comment: 34 pages, 18 figure

Assessment of Financial Risk Prediction Models with Multi-criteria Decision Making Methods

A wide range of classification models have been explored for financial risk prediction, but conclusions on which technique behaves better may vary when different performance evaluation measures are employed. Accordingly, this paper proposes the use of multiple criteria decision making tools in order to give a ranking of algorithms. More specifically, the selection of the most appropriate credit risk prediction method is here modeled as a multi-criteria decision making problem that involves a number of performance measures (criteria) and classification techniques (alternatives). An empirical study is carried out to evaluate the performance of ten algorithms over six real-life credit risk data sets. The results reveal that the use of a unique performance measure may lead to unreliable conclusions, whereas this situation can be overcome by the application of multi-criteria decision making techniques

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

Nontrivial Dynamics in the Early Stages of Inflation

Inflationary cosmologies, regarded as dynamical systems, have rather simple asymptotic behavior, insofar as the cosmic baldness principle holds. Nevertheless, in the early stages of an inflationary process, the dynamical behavior may be very complex. In this paper, we show how even a simple inflationary scenario, based on Linde's ``chaotic inflation'' proposal, manifests nontrivial dynamical effects such as the breakup of invariant tori, formation of cantori and Arnol'd's diffusion. The relevance of such effects is highlighted by the fact that even the occurrence or not of inflation in a given Universe is dependent upon them.Comment: 26 pages, Latex, 9 Figures available on request, GTCRG-94-1