Estimating Default Probabilities Research Articles

Variable Selection for Credit Risk Model Using Data Mining technique

With the emergence of the current financial crisis, societies see the increasing importance of credit risks management in financial institutions. Four mainstream credit risk rating models have been developed, however, their applicability in the Taiwan market is yet to be evaluated. In this paper, six major credit risk models, including Merton Option Pricing Model,Discriminant Analysis Model, Logistic Regression (Logit) Model, Probit Model, Survival Analysis Model, and Artificial Neural Network Model were examined, in order to identify the common variables applicable to each model. The common variables were then applied to each respective model directly. Using Transition Matrix and mapping methods to estimate long term default probability, for developing appropriate credit risk model with the estimated default probability.

Validation of credit default probabilities using multiple-testing procedures

We consider the problem of identifying inaccurate default probability estimates in credit rating systems. Since the validation of these estimates usually entails performing multiple tests, there is an increased risk of erroneously dismissing correctly calibrated default probabilities. We use multiple-testing procedures to control this risk of committing type-I errors as measured by the family-wise error rate (FWER) and the false discovery rate for finite sample sizes. For the FWER, we also consider procedures that take possible discreteness of the data (and the test statistics) into account. The performance of these methods is illustrated in a simulation setting and for empirical default data. The results show that both types of multiple-testing procedure can serve as helpful tools for identifying inaccurate estimates while maintaining a predefined level of type-I error.

The Distress Premium Puzzle

Fama and French (1992) suggest that the positive value premium results from financial distress risk. However, recent empirical research finds that financially distressed firms have lower stock returns, by using empirical estimates of default probabilities. This paper reconciles the positive value premium and the negative distress premium in a model that decouples actual and risk-neutral default probabilities. Moreover, in agreement with the data, firms with higher bond yields have higher stock returns in the model. The model also captures the fact that book-to-market dominates financial leverage in explaining stock returns. Finally, the model makes the prediction that the firms with higher risk-neutral default probabilities should have higher stock returns, which can be tested using credit-default-swap premiums.

Fuzzy Support Vector Machine for bankruptcy prediction

Bankruptcy prediction has been a topic of active research for business and corporate organizations since past few decades. The problem has been tackled using various models viz., Statistical, Market Based and Computational Intelligence in the past. Among Computational Intelligence models, Artificial Neural Network has become dominant modeling paradigm. In this Paper, we use a novel Soft Computing tool viz., Fuzzy Support Vector Machine (FSVM) to solve bankruptcy prediction problem. Support Vector Machine is a powerful statistical classification technique based on the idea of Structural Risk Minimization. Fuzzy Sets are capable of handling uncertainty and impreciseness in corporate data. Thus, using the advantage of Machine Learning and Fuzzy Sets prediction accuracy of whole model is enhanced. FSVM is implemented for analyzing predictors as financial ratios. A method of adapting it to default probability estimation is proposed. The test dataset comprises of 50 largest bankrupt organizations with capitalization of no less than $1 billion that filed for protection against creditors under Chapter 11 of United States Bankruptcy Code in 2001–2002 after stock marked crash of 2000. Experimental results on FSVM illustrate that it is better capable of extracting useful information from corporate data. This is followed by a comparative study of FSVM with other approaches. FSVM is effective in finding optimal feature subset and parameters. This is evident from the results thus improving prediction of bankruptcy. The choice of feature subset has positive influence on appropriate kernel parameters and vice versa which demonstrate its appreciable generalization performance than traditional bankruptcy prediction methods. Choosing appropriate value of parameter plays an important role on the performance of FSVM model. The effect of variability in prediction performance of FSVM with respect to various values of different parameters of SVM is also investigated. Finally, a comparative study of clustering power of FSVM is made with PNN on ripley and bankruptcy datasets. The results show that FSVM has superior clustering power than PNN.

Credit risk prediction using support vector machines

The main purpose of this paper is to examine the relative performance between least-squares support vector machines and logistic regression models for default classification and default probability estimation. The financial ratios from a data set of more than 78,000 financial statements from 2000 to 2006 are used as default indicators. The main focus of this paper is on the influence of small training samples and high variance of the financial input data and the classification performance measured by the area under the receiver operating characteristic. The resolution and the reliability of the predicted default probabilities are evaluated by decompositions of the Brier score. It is shown that support vector machines significantly outperform logistic regression models, particularly under the condition of small training samples and high variance of the input data.

Probability of default estimation and validation within the context of the credit cycle

The dependency of the individual default behavior of a firm on the state of the credit cycle is widely implemented in credit portfolio models and ultimately reflected in the Basel II one-factor model determining capital requirements. Despite this, macroeconomic variables able to represent this one factor – accounting for fluctuations in annual default rates – are not clearly identified. This paper analyzes non-parametric estimates of the credit cycle and macroeconomic variables are identified to explain systematic fluctuations in annual default rates, ie, the credit cycle. Applications of the presented methodology are in the area of default probability estimation and validation.

Determinants of Sovereign Risk: Macroeconomic Fundamentals and the Pricing of Sovereign Debt*

This paper investigates the effects of macroeconomic fundamentals on emerging market sovereign credit spreads. We find that the volatility of terms of trade in particular has a statistically and economically significant effect on spreads. This is robust to instrumenting terms of trade with a country-specific commodity price index. Our measures of country fundamentals have substantial explanatory power, even controlling for global factors and credit ratings. We also estimate default probabilities in a hazard model and find that model implied spreads capture a significant part of the variation in observed spreads out-of-sample. The fit is better for lower credit quality borrowers.

Sovereign Risk and Macroeconomic Fluctuations in an Emerging Market Economy

This paper assesses the role of sovereign risk in explaining macroeconomic fluctuations in Turkey. We estimate two versions of a simple New Keynesian small open economy model on quarterly data for the period 1994Q3-2008Q2: A basic version and a version augmented by a default premium on government debt due to a perceived risk of sovereign debt default. Model comparisons clearly support the augmented version since it leads to stronger internal propagation and hence smaller shocks are required in order to reconcile the observed dynamics of nominal and real variables, leading to better forecasting performance. The estimated default probability is highly debt-elastic, indicating that default fears are a relevant concern. The results suggest that the augmented model may lead to a better understanding of macroeconomic fluctuations in emerging market economies that are subject to sovereign risk. In terms of policy implications, counterfactual experiments show that both more active monetary policy and stronger fiscal feedbacks from debt on taxes can lead to less volatile inflation and debt dynamics, but higher debt feedbacks on taxation additionally reduce expected default rates.

Editor’s Letter

In the midst of this recession, there is a great deal of uncertainty over the extent of forthcoming corporate defaults. In this issue of The Journal of Fixed Income , we begin with an article by Padma Kadiyala and Sugato Chakravarty concerning the estimation of default probability and the recovery

Choice of Rating Technology and Loan Pricing in Imperfect Credit Markets

Accurate rating systems are of central importance for banks to price and manage their loan portfolios. A bank’s choice to invest in a more accurate rating technology is based on a trade-off: the better rating system usually comes at higher cost, but endows the bank with a competitive advantage, which includes potentially better access to funds. This paper models the rating technology choice of a bank as a two-stage game in an oligopolistic banking sector. In the first stage banks choose between two alternative rating technologies that provide estimates about a borrower’s default probability with varying precision. In the second stage banks set their loan prices based on estimated default probabilities in an imperfectly competitive loan market. While rating technology investment is lumpy and characterized by fixed costs, loan prices vary continuously with their markup over the risk-free rate of interest. The interaction of loan pricing and rating technology investment gives rise to the following predictions: equilibrium adoption of the new rating technology need not increase individual banks’ profits; identical banks in a symmetric banking sector might adopt the more accurate rating technologies sequentially rather than simultaneously; and increased competition in the banking sector slows investment in the new rating technology.

Default estimation for low-default portfolios

Risk managers at financial institutions are concerned with estimating default probabilities for asset groups both for internal risk control procedures and for regulatory compliance. Low-default assets pose an estimation problem that has attracted recent concern. The problem in default probability estimation for low-default portfolios is that there is little relevant historical data information. No amount of data data-processing can fix this problem. More information is required. Incorporating expert opinion formally is an attractive option. The probability (Bayesian) approach is proposed, its feasibility demonstrated, and its relation to supervisory requirements discussed.

Estimation of default probabilities using incomplete contracts data

This paper develops a count data model for credit scoring which allows the estimation of default probabilities using incomplete contracts data. The main advantage of the proposed approach is that it permits a more efficient use of the data, including that for the most recent clients. Moreover, because the probability of default is specified as a function of the age of the contract, the model provides some information on the timing of the defaults. The model is based on the beta-binomial distribution, which is found to be particularly adequate for this purpose. A well-known dataset on personal loans is used to illustrate the application of the proposed model.

A Latent Variable Approach to Validate Credit Rating Systems

We suggest a new parametric framework to assess the accuracy of estimated default probabilities (PDs). Whereas the traditional methods to validate credit rating systems focus primarily on the discriminatory power, recent advances in credit risk management and banking regulation has shifted the focus of rating validation to the accuracy of PD estimates. In this paper we introduce bank and obligor specific error terms which are additive to a suitably transformed latent variable, which in our approach has the interpretation of the true, unobservable PD of the underlying obligor. Provided with rating information from different sources (e.g., banks, rating tools, or rating agencies) and an appropriate model for the distribution of the latent PDs the parameters of the errors distribution can be obtained. In a specific application we assume the error terms to be jointly normal and estimate this model for a data set provided by the Austrian central bank where we observe PD estimates for 2090 obligors provided by 13 banks.

The pricing of conditional performance guarantees with risky collateral

Conditional performance guarantees with risky collaterals are specific bonding instruments that are not credit extensions or require only a service fee. Instead, they resemble a credit default swap (CDS) that is essentially an insurance contract and can thus be priced accordingly. A CDS‐based model is proposed here for pricing these instruments. The model incorporates both contractor default probability and the recovery risk of collateral. It also allows for explicit specification of bonding parameters such as the promised amount of payment in the event of default. For model implementation, a quasi‐KMV–Merton approach is proposed for the estimation of contractor default probability. The historical market prices and basic accounting data of publicly traded construction firms in the Taiwan Economic Journal Database (TEJD) are used to test the model. The model demonstrates effective statistical power to distinguish categorized samples of the firms. It shows that the current industrial practice of asking a standard service rate of 1% tends to charge too little for financially distressed firms and too much for normal ones.

Random Survival Forests Models for SME Credit Risk Measurement

This paper extends the existing literature on empirical research in the field of credit risk default for Small Medium Enterprizes (SMEs). We propose a non-parametric approach based on Random Survival Forests (RSF) and we compare its performance with a standard logit model. To the authors’ knowledge, no studies in the area of credit risk default for SMEs have used a variety of statistical methodologies to test the reliability of their predictions and to compare their performance against one another. As for the in-sample results, we find that our non-parametric model performs much better that the classical logit model. As for the out-of-sample performances, the evidence is just the opposite, and the logit performs better than the RSF model. We explain this evidence by showing how error in the estimates of default probabilities can affect classification error when the estimates are used in a classification rule.

Estimating Default Probabilities Implicit in Commercial Mortgage Backed Securities (CMBS)

This paper uses a structural credit risk model, providing an analytical formula to estimate default probabilities implicit in commercial mortgage backed security prices. Empirical studies on CMBS default have focused on the probability of default depending on loan characteristics at the origination and market indices. Recent studies show that unobservable current loan-to-value (LTV) ratio is a key state variable driving default. We update this variable using Real Estate Investment Trust (REIT) property-type indices over time. Later, we employ first passage time approach to study CMBS default using implied LTV.

Modeling dependencies between rating categories and their effects on prediction in a credit risk portfolio

AbstractThe internal‐rating‐based Basel II approach increases the need for the development of more realistic default probability models. In this paper, we follow the approach taken in McNeil A and Wendin J 7 (J. Empirical Finance 2007) by constructing generalized linear mixed models for estimating default probabilities from annual data on companies with different credit ratings. The models considered, in contrast to McNeil A and Wendin J 7 (J. Empirical Finance 2007), allow parsimonious parametric models to capture simultaneously dependencies of the default probabilities on time and credit ratings. Macro‐economic variables can also be included. Estimation of all model parameters are facilitated with a Bayesian approach using Markov chain Monte Carlo methods. Special emphasis is given to the investigation of predictive capabilities of the models considered. In particular, predictable model specifications are used. The empirical study using default data from Standard and Poor's gives evidence that the correlation between credit ratings further apart decreases and is higher than the one induced by the autoregressive time dynamics. Copyright © 2008 John Wiley & Sons, Ltd.

The Performance of Option-Based Default Risk Models on Commercial Mortgages

This article applies the first-passage-time approach to estimating default probabilities of commercial mortgages and empirically tests the cash flow proposition of Vandell (1995) by Receiver Operating Characteristic (ROC) technique. The focus is on comparing default predicting performance between a single trigger model and a double-trigger model. Using 17,616 lockout commercial loans issued between 1995 and 2001, we find the property value model performs the best. For mortgage underwriters, this empirical evidence suggests that while dealing with low-quality loans, liquidity risk measured by debt coverage ratio, rather than loan-to-value ratio, should be the key factor affecting borrowers9 default decisions. <b>TOPICS:</b>CMBS and commercial mortgage loans, credit risk management, analysis of individual factors/risk premia

Estimating Default Probabilities of Emerging Market Sovereigns: A New Look at a Not-so-New Literature

The January 2001 proposal for a New Basel Capital Accord has renewed the interest in obtaining default probabilities for various types of borrowers. This paper uses a panel logit model to estimate default probabilities of 78 emerging market countries (1984-97) as a function of a set of economic and political variables. These sovereign default probabilities are then compared with the default rates associated with the sovereign credit ratings of the two major rating agencies, Moody's Investors Service and Standard & Poor's. Unlike the existing literature, we define the dependent variable (sovereign default) differently, using the changes in the levels of debt arrears and amounts rescheduled as criteria instead of the levels themselves. The paper finds, first, that the most important determinants of sovereign default appear to be the past repayment performance of a country, the cost of international credit, the volatility of per capita income, and political risks. Second, the comparison of estimated default probabilities with rating agencies' default rates gives some preliminary evidence that the latter seem to considerably underestimate sovereign default risk. In other words, sovereign credit ratings appear to be to high on average.

Calibrating asset correlation for Indian corporate exposures

PurposeThis paper is a first attempt to empirically calibrate the default and asset correlation for large companies in India and elaborate its implications for credit risk capital estimation for a bank.Design/methodology/approachThe authors estimate default probabilities and default correlations of long‐term bonds of 542 Indian corporates using rating transitions and pair‐wise migrations over ten year cohorts of firms. Further, the implicit asset correlation from the estimated default correlations and default thresholds are derived using the asymptotic single risk factor approach.FindingsThe authors find evidence that default correlations are time variant and vary across rating grades and industries. The highest correlations are observed between companies within the same rating grades (systematic risk impact) and within the same industry (industry specific impact). More interestingly, significantly smooth monotonic relationship between the probability of default (PD) and asset correlation as prescribed by the Basel II IRB document (2006) are not found. Moreover, it is found that the asset correlation range for Indian corporates do not match with what is prescribed for corporate exposures by BCBS.Originality/valueThe authors address the dilemma implied by the negative relationship between PD and asset correlation as suggested by BCBS IRB formula and other research for developed economies with estimates of asset correlation for and emerging market like India and demonstrate its implications on the estimation of credit risk capital.