Low Default Portfolios Research Articles

Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche

This article gives a probabilistic overview of the widely used method of default probability estimation proposed by K. Pluto and D. Tasche. There are listed detailed assumptions and derivation of the inequality where the probability of default is involved under the influence of systematic factor. The author anticipates adding more clarity, especially for early career analysts or scholars, regarding the assumption of borrowers' independence, conditional independence, and interaction between the probability distributions such as binomial, beta, normal, and others. There is also shown the relation between the probability of default and the joint distribution of \sqrt{ϱ}X - \sqrt{1-ϱ}Y, where X, including but not limiting, is the standard normal, Y admits, including but not limiting, the beta-normal distribution and X, Y are independent.

Low Default Portfolios—A Proposed Rule to Identify Differences between Imprudence, Conservatism, and Exaggeration

Internal models may be used by banks to calculate their regulatory capital for credit risk. There are a variety of methodologies for estimating default probabilities, which leads to major differences in credit provisions and capital requirements. Using either a classical or a Bayesian technique, the computation of default probabilities can be ensured. Reduced form models are a choice. These models, however, might not be used to quantify economic capital because they assume independence among default events. Banks are compelled to employ structural models since defaults in the real world of banking are not solely due to exogenous causes. Because of the diversification effects between credit losses for one obligor and credit losses for other obligors in each bank’s portfolio, total unexpected losses do not equal the sum of individual unexpected losses. Those two types of models—reduced form and structural—are provided in either a theoretical or a numerical format. This paper covers both the classical and Bayesian techniques, with the latter employing a broader set of prior functions that offer considerably different probabilities. Distinguishing between imprudence, conservatism, and exaggeration might be difficult in the context of low default portfolios with scarce data. A realistic rule is proposed for finding the minimum and maximum bounds and therefore assessing the required conservatism margin by comparing classical and Bayesian probabilities.

Low Default Portfolios in Basel II and Basel III as a Special Case of Significantly Unbalanced Classes in Binary Choice Models

In contemporary world, binary choice models are used in many areas. However, for all such areas, a problem arises when the share of one of the classes in the data sample is small. If this share is significantly small, this class is referred to as low default class. The purpose of this paper is to examine the definitions of such a portfolio and the approaches to building models on its basis. Although various methods exist for obtaining results, this paper shows that distinguishing a low default portfolio class, on the one hand, benefits banks, as does any more detailed segmentation, but, on the other hand, it deteriorates the statistical properties of the models for the probability of default. It is therefore justified that for the internal rating based approach in the framework of Basel II and Basel III the regulator should require that banks build their models based on combined data sets discouraging them from setting excessive low default portfolio classes.

A multicriteria forecast of the default probability in credit risk assessment

This study analyses, through a multicriteria approach producing if-then rules, the possibility of forecasting the default probability (PD) for low-default portfolios in credit risk assessment. This approach relies on the simultaneous and complementary application of fuzzy and rough sets theories. The calculation of this probability is normally subject to judgments of experts, which imply subjectivity, imprecision and uncertainty of the results. In the proposed approach, the inferred if-then rules for a decision table generated by a simulation of 50 companies allowed the production of a knowledge base for the forecasting of classes of default probabilities. The 'RoughSets®' package, in 'R', was used as support for the analysis and forecasting system.

Estimating the Probability of Default for No-Default and Low-Default Portfolios

SummaryThe paper proposes a sequential Bayesian updating approach to estimate default probabilities on rating grade level for no- and low-default portfolios. Bayesian sequential updating enables default probabilities to be obtained also for those rating grades for which no defaults have been observed. The advantage of this approach is that it preserves the rank order of rating grades in the case of no defaults. Rank preservation is not ensured when using an identical prior distribution across all rating grades. We discuss Bayesian sequential updating for the beta–binomial model and a model incorporating the asymptotic single-risk factor model of the Basel Accord. Practical aspects such as incorporating information from external sources and the margin of conservatism are addressed.

Estimating the Probability of Default for No-Default and Low-Default Portfolios

This article proposes a sequential Bayesian updating approach to estimate default probabilities on rating grade level for no- and low-default portfolios. Bayesian sequential updating allows to obtain default probabilities also for those rating grades for which no defaults have been observed. The advantage of the proposed approach is that it preserves the rank order of rating grades in case of no defaults. Rank-preservation is not ensured when using an identical prior distribution across all rating grades. We discuss Bayesian sequential updating for the beta-binomial model and a model incorporating the asymptotic single risk factor model of the Basel Accord. Practical aspects such as incorporating information from external sources and the margin of conservatism are addressed.

Weight of the Default Component of CDS Spreads: Avoiding Procyclicality in Credit Loss Provisioning Framework

The current expected loss calculations have recently attracted considerable attention in the research on credit risk modeling, impairment provisioning, and financial networks’ stability. A new CDS‐based approach to estimate current expected credit loss is proposed for low default portfolios, containing credit exposures to corporate issuers covered by publicly traded CDS contracts. First, a fraction of CDS spread related to a pure default compensation for different CDS maturities is assessed. Our results contrast with previous research. Second, based on the obtained historical weights of the default risk premium, a forward‐looking term structure of the probabilities of default implied by the current CDS quotes is derived. The proposed approach covers both investment and noninvestment grade debt. The resulting framework is applied to a sample of corporate bonds. The developed methodology provides a useful tool, on one hand, for credit risk managers and balance‐sheet preparers and, on the other hand, for regulators of financial markets as it sheds light on how procyclicality could be avoided in provisions.

Modelling European sovereign default probabilities with copulas

The goal of this article is to investigate a dependence among sovereign countries’ risk of default. The analysis was based on data for 42 European countries during the period 1994–2013. Three models were used to calculate default probabilities: Li’s based on transition matrix and prudent unconditional and conditional on previous defaults estimation technique for low default portfolios. The relationship was analysed through the use of different types of copulas. The analysis has shown no regularity in a selection of the optimal copula. The results differ based on the model and rating grade combination used.

Investigating the missing data effect on credit scoring rule based models: The case of an Iranian bank

Credit risk management is a process in which banks estimate probability of default (PD) for each loan applicant. Data sets of previous loan applicants are built by gathering their data, and these internal data sets are usually completed using external credit bureau’s data and finally used for estimating PD in banks. There is also a continuous interest for bank to use rule based classifiers to build their default prediction models. However, in practice the data records are usually incomplete and have some missing values and this make problems for banks, especially in credit risk portfolios which are low default and makes model rule based building complex. Several strategies could be used in order to handle the missing data issue. This paper used five missing value handling strategies including; ignoring, replacing with random, mean, C&R tree induced values and elimination strategies in a real credit scoring dataset. Experimental results show that ignoring strategy consistently outperforms other methods on test data set, and suggest that the CHAID is a useful classifier for handling low default portfolios with missing value.

The loss given default of a low-default portfolio with weak contagion

In this paper we study the loss given default (LGD) of a low default portfolio (LDP), assuming that there is weak credit contagion among the obligors. We characterize the credit contagion by a Sarmanov dependence structure of the risk factors that drive the obligors’ default, where the risk factors are assumed to be heavy tailed. From a new perspective of asymptotic analysis, we derive a limiting distribution for the LGD. As a consequence, an approximation for the entire distribution, in contrast to just the tail behavior, of the LGD is obtained. We show numerical examples to demonstrate the limiting distribution. We also discuss possible applications of the limiting distribution to the calculation of moments and the Value at Risk (VaR) of the LGD.

Endogenous Derivation and Forecast of Lifetime PDs

This paper proposes a simple technical approach for the derivation of future (forward) point-in-time PD forecasts, with minimal data requirements. The inputs required are the current and future through-the-cycle PDs of the obligors, their last known default rates, and a measure for the systematic dependence of the obligors. Technically, the forecasts are made from within a classical asset-based credit portfolio model, just with the assumption of a suitable autoregressive process for the systematic factor. The paper discusses in detail the practical issues of implementation, in particular the parametrization alternatives.The paper also shows how the approach can be naturally extended to low-default portfolios with volatile default rates, using Bayesian methodology. Furthermore, the expert judgments about the current macroeconomic state, although not necessary for the forecasts, can be embedded using the Bayesian technique.The presented forward PDs can be used for the derivation of lifetime credit losses required by the new accounting standard IFRS 9. In doing so, the presented approach is endogenous, as it does not require any exogenous macroeconomic forecasts which are notoriously unreliable and often subjective.

Objective Bayesian Estimation of the Probability of Default

Summary Reliable estimation of the probability of default (PD) of a customer is one of the most important tasks in credit risk modelling for banks applying the internal ratings-based approach under the Basel II–III framework. Motivated by the desire to analyse reliably a low default portfolio of non-profit housing companies, we consider PD estimation within a Bayesian framework and develop objective priors for the parameter θ representing the PD in the Gaussian and the Student t single-factor models. A marginal reference prior and limiting versions of it are presented and their posterior propriety is studied. The priors are shown to be direct generalizations of the Jeffreys prior in the binomial model. We use Markov chain Monte Carlo strategies to sample efficiently from the posterior distributions and compare the developed priors on the grounds of the frequentist properties of the resulting Bayesian inferences with subjective priors previously proposed in the literature. Finally, the analysis of the non-profit housing companies portfolio highlights the ultility of the methodological developments.

The Assessment of the Default Risk for the Banks of the Romanian Banking System

By the current study we analyze the performance and plausibility of the empirical results provided by the [5] Duffie and Lando (2001) credit risk structural model with asymmetric information. By construction, such a model can allow the endogenous understanding of the default event (typically for a structural model), the plausibility of the default intensity existence (typically for a reduced form model), as well as the tractability of analytical formulas to be used at the estimation of the credit risk parameters. Under this framework we analyze the empirical model results, by the quantitative creditworthiness assessment of the banks from the Romanian banking system, as financial institutions of a low default portfolio. For the model implementation we apply a special calibration approach for the accounting white noise parameter. The empirical study is being conducted by the use of the banks’ financial statement time series over the last Romanian economic cycle, during the period 2002 – 2012.

Optimization of Post-Scoring Classification and Impact on Regulatory Capital for Low Default Portfolios

After the crisis of 2008, new regulatory requirements have emerged with supervisors strengthening their position in terms of requirements to meet IRBA standards. Low Default Portfolios (LDP) present specific characteristics that raise challenges for banks when building and implementing credit risk models. In this context, where banks are looking to improve their Return On Equity and supervisors strengthening their positions, this paper aims to provide clues for optimizing Post-Scoring classification as well as analyzing the relationship between the number of classes in a rating scale and the impact on regulatory capital for LDPs.

Extending Multi-Period Pluto and Tasche PD Calibration Model Using Mode LRDF Approach

The intention of this paper is to propose extension to the Pluto and Tasche PD calibration model for low default portfolios that could produce more stable LRDF estimates and eliminate the necessity of quartile choice, while preserving adequate level of conservatism. Multi-period Pluto and Tasche model allows us to fulfill Basel committee requirements regarding long-term LRDF calibration even for portfolios with no observable defaults. The main drawback of that approach is a very strict requirement for the sample: only borrowers that are observable to the bank within each point on long-term horizon could be used as observations. Information regarding rating migrations, borrowers that arrived in the portfolio after sample cutoff date and borrowers that left the portfolio before the end of long-term calibration horizon should be excluded from the sample. Proposed Mode approach pairs Pluto and Tasche model with mode LRDF estimator (proposed by Canadian OSFI), as the results, it eliminates drawbacks of the original Pluto and Tasche model.

Bayesian confidence intervals for probability of default and asset correlation of portfolio credit risk

We derive Bayesian confidence intervals for the probability of default (PD), asset correlation (Rho), and serial dependence (Theta) for low default portfolios (LDPs). The goal is to reduce the probability of underestimating credit risk in LDPs. We adopt a generalized method of moments with continuous updating to estimate prior distributions for PD and Rho from historical default data. The method is based on a Bayesian approach without expert opinions. A Markov chain Monte Carlo technique, namely, the Gibbs sampler, is also applied. The performance of the estimation results for LDPs validated by Monte Carlo simulations. Empirical studies on Standard & Poor's historical default data are also conducted.

Bayesian estimation of probabilities of default for low default portfolios

The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well-established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the estimation. The Bayesian estimator for the PD based on the uninformed, uniform prior distribution is an obvious alternative that avoids the choice of a confidence level. It is demonstrated in this paper that in the case of independent default events the upper confidence bounds can be represented as quantiles of a Bayesian posterior distribution based on a prior that is slightly more conservative than the uninformed prior. The paper then describes how to implement the uninformed and conservative Bayesian estimators in the dependent one- and multi-period default data cases and compares their estimates with the upper confidence bound estimates. The comparison leads to a suggestion of a constrained version of the uninformed (neutral) Bayesian estimator as an alternative to the upper confidence bound estimators.

Are Default Probability Models Relevant for Low Default Portfolios?

The aim of this paper is to address the validity of default probability models calibrated on a dataset including a very low (or none) number of defaults. The few approaches, proposed by the specialized literature are based on the confidence intervals computed via probabilistic, Bayesian or analytic methods. We propose a benchmark of these methods and we explore the cases for which they are the most suited for. We propose a new method for computing the upper bound of the default probability in low default portfolios, employing resampling approaches. For the special case of no default portfolios we investigate an adjustment based on non-Gaussian behavior of the distance to default. We address also the issue concerning the dependency between defaults using non-Gaussian copulas.

Using semi-supervised classifiers for credit scoring

In credit scoring, low-default portfolios (LDPs) are those for which very little default history exists. This makes it problematic for financial institutions to estimate a reliable probability of a customer defaulting on a loan. Banking regulation (Basel II Capital Accord), and best practice, however, necessitate an accurate and valid estimate of the probability of default. In this article the suitability of semi-supervised one-class classification (OCC) algorithms as a solution to the LDP problem is evaluated. The performance of OCC algorithms is compared with the performance of supervised two-class classification algorithms. This study also investigates the suitability of over sampling, which is a common approach to dealing with LDPs. Assessment of the performance of one- and two-class classification algorithms using nine real-world banking data sets, which have been modified to replicate LDPs, is provided. Our results demonstrate that only in the near or complete absence of defaulters should semi-supervised OCC algorithms be used instead of supervised two-class classification algorithms. Furthermore, we demonstrate for data sets whose class labels are unevenly distributed that optimising the threshold value on classifier output yields, in many cases, an improvement in classification performance. Finally, our results suggest that oversampling produces no overall improvement to the best performing two-class classification algorithms.

Bayesian Estimation of Probabilities of Default for Low Default Portfolios

The estimation of probabilities of default (PDs) for low default portfolios by means of upper confidence bounds is a well established procedure in many financial institutions. However, there are often discussions within the institutions or between institutions and supervisors about which confidence level to use for the estimation. The Bayesian estimator for the PD based on the uninformed, uniform prior distribution is an obvious alternative that avoids the choice of a confidence level. In this paper, we demonstrate that in the case of independent default events the upper confidence bounds can be represented as quantiles of a Bayesian posterior distribution based on a prior that is slightly more conservative than the uninformed prior. We then describe how to implement the uninformed and conservative Bayesian estimators in the dependent one- and multi-period default data cases and compare their estimates to the upper confidence bound estimates. The comparison leads us to suggest a constrained version of the uninformed (neutral) Bayesian estimator as an alternative to the upper confidence bound estimators.