Basel II compliant credit risk modelling: model development for imbalanced credit scoring data sets, loss given default (LGD) and exposure at default (EAD)

The purpose of this thesis is to determine and to better inform industry practitioners to the most appropriate classification and regression techniques for modelling the three key credit risk components of the Basel II minimum capital requirement; probability of default (PD), loss given default (LGD), and exposure at default (EAD). The Basel II accord regulates risk and capital management requirements to ensure that a bank holds enough capital proportional to the exposed risk of its lending practices. Under the advanced internal ratings based (IRB) approach Basel II allows banks to develop their own empirical models based on historical data for each of PD, LGD and EAD.In this thesis, first the issue of imbalanced credit scoring data sets, a special case of PD modelling where the number of defaulting observations in a data set is much lower than the number of observations that do not default, is identified, and the suitability of various classification techniques are analysed and presented. As well as using traditional classification techniques this thesis also explores the suitability of gradient boosting, least square support vector machines and random forests as a form of classification. The second part of this thesis focuses on the prediction of LGD, which measures the economic loss, expressed as a percentage of the exposure, in case of default. In this thesis, various state-of-the-art regression techniques to model LGD are considered. In the final part of this thesis we investigate models for predicting the exposure at default (EAD). For off-balance-sheet items (for example credit cards) to calculate the EAD one requires the committed but unused loan amount times a credit conversion factor (CCF). Ordinary least squares (OLS), logistic and cumulative logistic regression models are analysed, as well as an OLS with Beta transformation model, with the main aim of finding the most robust and comprehensible model for the prediction of the CCF. Also a direct estimation of EAD, using an OLS model, will be analysed. All the models built and presented in this thesis have been applied to real-life data sets from major global banking institutions

Consumer finance: challenges for operational research

Consumer finance has become one of the most important areas of banking, both because of the amount of money being lent and the impact of such credit on global economy and the realisation that the credit crunch of 2008 was partly due to incorrect modelling of the risks in such lending. This paper reviews the development of credit scoring—the way of assessing risk in consumer finance—and what is meant by a credit score. It then outlines 10 challenges for Operational Research to support modelling in consumer finance. Some of these involve developing more robust risk assessment systems, whereas others are to expand the use of such modelling to deal with the current objectives of lenders and the new decisions they have to make in consumer finance. <br/

Operations research in consumer finance: challenges for operational research

Consumer finance has become one of the most important areas of banking both because of the amount of money being lent and the impact of such credit on the global economy and the realisation that the credit crunch of 2008 was partly due to incorrect modelling of the risks in such lending. This paper reviews the development of credit scoring,-the way of assessing risk in consumer finance- and what is meant by a credit score. It then outlines ten challenges for Operational Research to support modelling in consumer finance. Some of these are to developing more robust risk assessment systems while others are to expand the use of such modelling to deal with the current objectives of lenders and the new decisions they have to make in consumer financ

Modelling loss given default of corporate bonds and bank loans

Loss given default (LGD) modelling has become increasingly important for banks as they are required to comply with the Basel Accords for their internal computations of economic capital. Banks and financial institutions are encouraged to develop separate models for different types of products. In this thesis we apply and improve several new algorithms including support vector machine (SVM) techniques and mixed effects models to predict LGD for both corporate bonds and retail loans. SVM techniques are known to be powerful for classification problems and have been successfully applied to credit scoring and rating business. We improve the support vector regression models by modifying the SVR model to account for heterogeneity of bond seniorities to increase the predictive accuracy of LGD. We find the proposed improved versions of support vector regression techniques outperform other methods significantly at the aggregated level, and the support vector regression methods demonstrate significantly better predictive abilities compared with the other statistical models at the segmented level. To further investigate the impacts of unobservable firm heterogeneity on modelling recovery rates of corporate bonds a mixed effects model is considered, and we find that an obligor-varying linear factor model presents significant improvements in explaining the variations of recovery rates with a remarkably high intra-class correlation being observed. Our study emphasizes that the inclusion of an obligor-varying random effect term has effectively explained the unobservable firm level information shared by instruments of the same issuer. At last we incorporate the SVM techniques into a two-stage modelling framework to predict recovery rates of credit cards. The two-stage model with a support vector machine classifier is found to be advantageous on an out-of-time sample compared with other methods, suggesting that an SVM model is preferred to a logistic regression at the classification stage. We suggest that the choice of regression models is less influential in prediction of recovery rates than the choice of classification methods in the first step of two-stage models based on the empirical evidence. The risk weighted assets of financial institutions are determined by the estimates of LGD together with PD and EAD. A robust and accurate LGD model impacts banks when making business decisions including setting credit risk strategies and pricing credit products. The regulatory capital determined by the expected and unexpected losses is also important to the financial market stability which should be carefully examined by the regulators. In summary this research highlights the importance of LGD models and provides a new perspective for practitioners and regulators to manage credit risk quantitatively

European exchange trading funds trading with locally weighted support vector regression

In this paper, two different Locally Weighted Support Vector Regression (wSVR) algorithms are generated and applied to the task of forecasting and trading five European Exchange Traded Funds. The trading application covers the recent European Monetary Union debt crisis. The performance of the proposed models is benchmarked against traditional Support Vector Regression (SVR) models. The Radial Basis Function, the Wavelet and the Mahalanobis kernel are explored and tested as SVR kernels. Finally, a novel statistical SVR input selection procedure is introduced based on a principal component analysis and the Hansen, Lunde, and Nason (2011) model confidence test. The results demonstrate the superiority of the wSVR models over the traditional SVRs and of the v-SVR over the ε-SVR algorithms. We note that the performance of all models varies and considerably deteriorates in the peak of the debt crisis. In terms of the kernels, our results do not confirm the belief that the Radial Basis Function is the optimum choice for financial series

Tree Boosting Data Competitions with XGBoost

This Master's Degree Thesis objective is to provide understanding on how to approach a supervised learning predictive problem and illustrate it using a statistical/machine learning algorithm, Tree Boosting. A review of tree methodology is introduced in order to understand its evolution, since Classification and Regression Trees, followed by Bagging, Random Forest and, nowadays, Tree Boosting. The methodology is explained following the XGBoost implementation, which achieved state-of-the-art results in several data competitions. A framework for applied predictive modelling is explained with its proper concepts: objective function, regularization term, overfitting, hyperparameter tuning, k-fold cross validation and feature engineering. All these concepts are illustrated with a real dataset of videogame churn; used in a datathon competition

Pricing tranched credit products with generalized multifactor models

The market for tranched credit products (CDOs, Itraxx tranches) is one of the fastest growing segments in the credit derivatives industry. However, some assumptions underlying the standard Gaussian onefactor pricing model (homogeneity, single factor, Normality), which is the pricing standard widely used in the industry, are probably too restrictive. In this paper we generalize the standard model by means of a two by two model (two factors and two asset classes). We assume two driving factors (business cycle and industry) with independent tStudent distributions, respectively, and we allow the model to distinguish among portfolio assets classes. In order to illustrate the estimation of the parameters of the model, an empirical application with Moody's data is also included