Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 84-90). Also available in electronic version.

This thesis is concerned with statistical aspects of credit scoring, the process of determining how likely an applicant for credit is to default with repayments. In Chapters 1-4 a detailed introduction to credit scoring methodology is presented, including evaluation of previous published work on credit scoring and a review of discrimination and classification techniques. In Chapter 5 we describe different approaches to measuring the absolute and relative performance of credit scoring models. Two significance tests are proposed for comparing the bad rate amongst the accepts (or the error rate) from two classifiers. In Chapter 6 we consider different approaches to reject inference, the procedure of allocating class membership probabilities to the rejects. One reason for needing reject inference is to reduce the sample selection bias that results from using a sample consisting only of accepted applicants to build new scorecards. We show that the characteristic vectors for the rejects do not contain information about the parameters of the observed data likelihood, unless extra information or assumptions are included. Methods of reject inference which incorporate additional information are proposed. In Chapter 7 we make comparisons of a range of different parametric and nonparametric classification techniques for credit scoring: linear regression, logistic regression, projection pursuit regression, Poisson regression, decision trees and decision graphs. We conclude that classifier performance is fairly insensitive to the particular technique adopted. In Chapter 8 we describe the application of the k-NN method to credit scoring. We propose using an adjusted version of the Eucidean distance metric, which is designed to incorporate knowledge of class separation contained in the data. We evaluate properties of the k-NN classifier through empirical studies and make comparisons with existing techniques.

<p>Credit risk is the risk of losses due to the failure to fulfil the obliged payment from a debtor or a counterparty. It is one of the three major components of risks that a bank faces as defined in the new Basel Accord. The credit risk literature has experienced similar rapid growth as the credit market itself. There are currently four different approaches to analyzing credit risk: structural, reduced-form, incomplete information and hybrid models. Even though there are large volumes of published research papers and books on credit risk, our understanding and management skills in this area are still very limited as evidenced by the recent crash of the subprime market. This thesis combines three working papers on credit risk modeling and aims at adding some insights and contributions to the current credit risk literature.</p><p>In the first paper, we propose to randomize the initial condition of a generalized structural model, where the solvency ratio instead of the asset value is modeled explicitly. This initial randomization assumption is motivated by the fact that market players cannot observe the solvency ratio accurately. We find that positive short spreads can be produced due to imperfect observation on the risk factor. The two models we have considered, the Randomized Merton (RM)-II and the Randomized Black-Cox (RBC)-II, both have explicit expressions for Probability of Default (PD), Loss Given Default (LGD) and Credit Spreads (CS). In the RM-II model, both PD and LGD are found to be of order of √T, as the maturity T approaches zero. It therefore provides an example that has no well-defined default intensity but still admits positive short spreads. In the RBC-II model, the positive short spread is generated through the positive default intensity of the model. Because explicit formulas are available, these two Randomized Structure (RS) models are easily implemented and calibrated to the market data. This is illustrated by a calibration exercise on Ford Motor Corp. Credit Default Swap (CDS) spread data.</p> <p>In the second paper, we introduce the inverse-CIR (iCIR) intensity model of credit risk. A multi-firm intensity-based model is constructed where negative correlations are built through the negative correlation between the Cox-Ingersoll-Ross (CIR) process and its inverse. This parsimonious setting allows us to form rich correlation structures among short spreads of different firms, while keeping nonnegative conditions for interest rates and short spreads. The bond prices are given by explicit expressions involving confluent hypogeometric functions. This model can be regarded as an extension of the Ahn & Gao (1999) one factor iCIR model on interest rates to a multi-factor framework on credit risk.</p> <p> In the third paper, we derive several forms of the equity volatility as a function of the equity value, from the structural credit risk literature. We then propose a new jump to default model by taking the equity volatility to be of the form implied by the models of Leland (1994) and Leland & Toft (1996). This model involves a process we call the Dual-Jacobi process and which has explicit formulae for its moments. Gram-Charlier expansions are then applied to approximate bond and call prices. Our model generalizes Linetsky (2006) by incorporating a local volatility which is bounded below by a positive constant. This local volatility will decrease to a positive constant for increasing stock prices, making the stock process asymptotic to Geometric Brownian Motion (GBM). In this sence, our model is more realistic than Constant Elasticity of Variance (CEV) models.</p> / Thesis / Doctor of Philosophy (PhD)

In recent years, issues about credit risk attract more and more attentions. This thesis provides some empirical evidence for the behavior of credit spreads in Taiwan based on a Markov model proposed by Jarrow, Lando, and Turnbull (1997). Although the estimated risk premium adjustments increases as the credit rating level goes downward, it does not exist robust relations between credit yield spreads and credit ratings. Apparently, the model does not fit the real condition well because of some structural factors and limitations. I try to suggest some possible explanations for this phenomenon. Despites some poor performances of this model, these results still offer some directions to reconsider the valuation of straight corporate bonds in Taiwan.

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Credit risk models widely used in the financial market nowadays assume that losses are normally distributed and have linear dependence. Nevertheless it is well known that asset returns (loans included) are not normally distributed and present tail dependence. Therefore the traditional approaches are not able to capture possible stronger association among higher losses and tend to underestimate the probability of joint extreme losses. Copula functions are an alternative to overcome this drawback since they yield accurate dependence measures regardless of the distribution of the variables analysed. This technique was first applied to credit risk in 2000 but the studies in this field have been concentrated on corporate debt and derivatives. We filled this gap in the literature by employing copulas to estimate the dependence among consumer loans. In an empirical study based on a credit card portfolio of a large UK bank, we found evidence that standard models are misspecified as the dependence across default rates in the dataset is seldom expressed by the (Gaussian) copula implicit in those models. The comparison between estimations of joint high default rates from the conventional approach and from the best-fit copulas confirmed the superiority of the latter method. The initial investigation concerning pairs of credit segments was extended to groups of three segments with the purpose of accounting for potential heterogeneous dependence within the portfolio. To do so, we introduced vine copulas (combinations of bivariate copulas to form high-dimension copulas) to credit risk and the empirical estimations of simultaneous excessive defaults based on this technique were better than both the estimations from the pairwise copulas and from the conventional models. Another contribution of this work concerns the application of copulas to a method derived from the limited credit models: the calculation of the capital required to cover unexpected losses in financial institutions. Two models were proposed and, according to simulations, outperformed the current method (Basel) in most of the scenarios considered.

The master thesis deals with the advanced methods for estimating credit risk parameters from market prices: probability of default (PD) and loss given default (LGD). Precise evaluation of these parameters is important not only for banks to calculate their regulatory capital but also for investors to price risky bonds and credit derivatives. We provide forward looking reduced-form analytical method for calculation of PD and LGD of corporate defaultable bonds based on their quoted market prices, prices of equivalent risk-free bonds and quoted credit default swap spreads of the issuer of these bonds. This is reversed to most of the studies on credit risk modeling, as aim is not to price instruments based on estimated credit risk parameters, but to calculate these parameters based on the available market prices. Furthermore, compared to other studies, the LGD parameter is assumed to be endogenous and we provide the method for its simultaneous calculation with the probability of default. Finally, using developed methods, we estimate implied PD and LGD for five European banks assuming that the risk is priced correctly by other investors and the markets are efficient. JEL Classification: C02, C63, G13, G33 Keywords: credit risk, loss given default, probability of default, credit default swap Author's...

This thesis is devoted to UK Mortgage Performance Modelling. The research conducted uses an option pricing methodology to model theoretically the value of Mortgages, the Option to default and the probability to default and to compare the predictive accuracy of the latter with the predictive accuracy of data driven credit-scoring techniques. Theoretical models are constructed to represent the life cycles of loans collateralised by real property operating within a stochastic economic environment of house-price and interest rate. These realistic mortgage models provide a confirmation of recent research based upon a relaxation of the assumption of financially rational, 'ruthless' prepayment, bridge a potential oversight in existing research by an extension of existing modelling in the stochastic behaviour of the house price process and present a proposal for a straightforward approach utilising characteristic measures of borrower delinquency and insolvency that enables estimation of the default probabilities implicit in residential mortgages using a simple but enhanced optimising structural model. This model straightforwardly demonstrates that one can predict the probability of eventual default, beginning at the origination of the loan, the time when a lender would be most interested in making such a determination. Secondly the problem of mortgage loan default risk is empirically assessed in a number of different ways focusing upon analysis of the competing risks of early termination, the inclusion of macro-economic variables - time varying covariates and unobserved borrower heterogeneity. Key insight is provided by means of a multi-period model exploiting the potential of the survival analysis approach when both loan survival times and the various regressors are measured at discrete points in time. The discrete-time hazard model is used as an empirical framework for analysing the deterioration process leading to loan default and as a tool for prediction of the same event. Results show that the prediction accuracy of the duration model is better than that provided by a single period logistic model. The predictive power of the discrete time survival analysis is enhanced when it is extended to allow for unobserved individual heterogeneity (frailty).

Defaulted retail mortgage loans as a percentage of retail mortgage loans and advances averaged 9 percent over 2010 as reported in the SARB Bank Supervision Annual report. Banks are in the business of risk taking and as a result need to constantly evaluate and review credit risk management to attain sustained profitability. In credit risk modelling, default risk is associated with client-specific factors particularly the client’s credit rating. However, Brent, Kelly, Lindsey-Taliefero, and Price (2011), have shown that variation in mortgage delinquencies reflect changes in general macroeconomic conditions. This study aims to provide evidence of whether macroeconomic factors such as the house price index, CPI, credit growth, debt to income ratio, prime interest rates, and unemployment, are key drivers of residential mortgage delinquencies and default in South Africa. In this study, data from an undisclosed bank is used to estimate three models that are supposed to capture the influence of several macroeconomic variables on 30 day, 60 day, and 90 day delinquency rates over the 2006-2010 period. In order to eliminate the potential bias introduced by those observations, a fourth model was estimated using aggregated banking industry published by the SARB. However, due to data constraints, only the severe mortgage delinquency state, that is the 90 day delinquency rate was modelled using this aggregate data. The SARB sample covers the period between 2008 and 2010. The choice of the date 2008 coincides with the introduction of the Basel 2 regulatory framework. Prior to 2008, the big four South African banks were governed by the Basel 1 framework, and measured their credit risk using the so-called Standardised Approach which has different loan categories and different default definitions compared to the Basel 2 Advanced Internal Ratings Approach adopted in 2008. The findings suggest that the two samples (i.e. the data from the individual bank and the SARB data) imply different explanatory macroeconomic factors. Prime interest rates were found to be the only important variable in determining 30 day and 60 day delinquency rates for the individual bank. The house price index, CPI, credit growth, and prime interest rates were found to be the main determinants of the 90 day delinquency rates for the undisclosed bank, while the house price index, CPI, and credit growth, determine the 90 day delinquency rates for the big four banks.

The expected yield to maturity on a defaultable obligation equals the nominal yield less expected default losses. However, in a mark-to-market world, one doesn't have the luxury of reporting one's performance on the basis of yield to maturity. Total return is calculated for an arbitrary holding period, and must reflect any mark-to-market gains or losses as at the close of the period-gains or losses that can be triggered by the bond's upgrade or downgrade. Thus to estimate expected total return, one must estimate not only expected default losses, but also the impact on capital price of expected ratings transitions. This paper begins with the observation that a bond which is blessed by more favourable transition characteristics is likely to produce a higher total return, and poses the question of how that benefit can be quantified. How much is it worth? To answer the question, I start by specifying a formal bond-pricing model reflective of ratings transitions. I survey various statistical methods and past research efforts to identify the ratings-transition matrix which best parametrises the model, and propose a novel test for selecting between competing matrices. Using this approach, I replicate several important studies of ratings transitions. I also use it to examine new published and unpublished data, testing for (and finding) ratings path-dependency, and otherwise exploring the effect of ratings changes on different bond sectors. I then turn to the question of whether it is possible to estimate bond-specific transition probabilities, and propose a way to do so. I combine these efforts into the specifications for a pricing model capable of answering the question: How much is it worth?