• The Korean Journal of Applied Statistics
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• v.21 no.6
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• pp.1065-1075
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• 2008

For the model validation of credit rating models, Kolmogorov-Smirnov(K-S) statistic has been widely used as a testing method of discriminatory power from the probabilities of default for default and non-default. For the credit rating works, K-S statistics are to test two identical distribution functions which are partitioned from a distribution. In this paper under the assumption that the distribution is known, modified K-S statistic which is formulated by using known distributions is proposed and compared K-S statistic.

• Journal of the Korean Data and Information Science Society
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• v.22 no.2
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• pp.149-157
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• 2011

Undecided inference could be regarded as a missing data problem such as MARand MNAR. Under the assumption of MAR, undecided inference make use of logistic regression model. The probability of default for the undecided group is obtained with regression coefficient vectors for the decided group and compare with the probability of default for the decided group. And under the assumption of MNAR, undecide dinference make use of logistic regression model with additional feature random vector. Simulation results based on two kinds of real data are obtained and compared. It is found that the misclassification rates are not much different from the rate of rawdata under the assumption of MAR. However the misclassification rates under the assumption of MNAR are less than those under the assumption of MAR, and as the ratio of the undecided group is increasing, the misclassification rates is decreasing.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.29-39
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• 2009

Among others, ROC and CAP curves are used to explore the discriminatory power between the defaults and non-defaults, based on the distribution of the probability of default in credit rating works. ROC and CAP curves are plotted in terms of various ratios of the probability of default. Each point on ROC and CAP curves is calculated according to cutting points (scores) for classifying between defaults and non-defaults. In this paper, adjusted ROC and CAP curves are proposed by using functions of ratios of the probability of default. It is possible to recognize the score corresponding to a point oil these adjusted curves, and we can identify the best score to show the optimal discriminatory power. Moreover, we discuss the relationships between the best score obtained from the adjusted ROC and CAP curves and the score corresponding to Kolmogorov - Smirnov statistic to test the homogeneous distribution functions of the defaults and non-defaults.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.253-268
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• 2011

In this paper, we estimate systematic risk from credit migration (or transition) matrices under "Asymptotic Single Risk Factor" model. We analyzed transition matrices issued by KR(Korea Ratings) and concluded that systematic risk implied on credit migration somewhat coincide with the real economic cycle. Especially, we found that systematic risk implied on credit migration is better than that implied on the default rate. We also emphasize how to conduct a stress test using systematic risk extracted from transition migration. We argue that the proposed method in this paper is better than the usual method that is only considered for the conditional probability of default(PD). We found that the expected loss critically increased when we explicitly consider the change of credit quality in a given portfolio, compared to the method considering only PD.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1289-1312
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• 2015

This paper studies the comovement of industry defaults among listed companies. Rank correlation coefficients of Spearman's ${\rho}$ and Kendall's ${\tau}$ measure the concordance of default. These non-parametric coefficients do not require distributional assumptions and are easily used even with less data and extreme values. This study predicts a future financial crisis by looking at the comovement of industry defaults. We expect our analyses will aid market participants (including company executives) in making investment or risk management decisions.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.911-921
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• 2009

Receiver Operating Characteristic(ROC) and Cumulative Accuracy Profile(CAP) curves are two methods used to assess the discriminatory power of different credit-rating approaches. The points of optimal classification accuracy on an ROC curve and of maximal profit on a CAP curve can be found by using iso-performance tangent lines, which are based on the standard notion of accuracy. In this paper, we offer an alternative accuracy measure called the true rate. Using this rate, one can obtain alternative optimal threshold points on both ROC and CAP curves. For most real populations of borrowers, the number of the defaults is much less than that of the non-defaults, and in such cases the true rate may be more efficient than the accuracy rate in terms of cost functions. Moreover, it is shown that both alternative scores of optimal classification accuracy and maximal profit are the identical, and this single score coincides with the score corresponding to Kolmogorov-Smirnov statistic used to test the homogeneous distribution functions of the defaults and non-defaults.

• Journal of Intelligence and Information Systems
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• v.9 no.1
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• pp.227-249
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• 2003

Prediction of corporate failure using past financial data is a well-documented topic. Early studies of bankruptcy prediction used statistical techniques such as multiple discriminant analysis, logit and probit. Recently, however, numerous studies have demonstrated that artificial intelligence such as neural networks can be an alternative methodology for classification problems to which traditional statistical methods have long been applied. In building neural network model, the selection of independent and dependent variables should be approached with great care and should be treated as model construction process. Irrespective of the efficiency of a teaming procedure in terms of convergence, generalization and stability, the ultimate performance of the estimator will depend on the relevance of the selected input variables and the quality of the data used. Approaches developed in statistical methods such as correlation analysis and stepwise selection method are often very useful. These methods, however, may not be the optimal ones for the development of neural network model. In this paper, we propose a genetic algorithms approach to find an optimal or near optimal input variables fur neural network modeling. The proposed approach is demonstrated by applications to bankruptcy prediction modeling. Our experimental results show that this approach increases overall classification accuracy rate significantly.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.407-417
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• 2010

In Basel II compliance, internal rating systems are allowed for banks to enhance the self control and the validation of the system are getting more important. The validation methods are composed of qualitative test and quantitative test, three basic standards of which are discriminatory power, stability and calibration. The aim of this article is to review the quantitative tests for calibration and find a new method for it. These methods for discrimination between forecasted PD and observed PD include binomial test, chi square test, Brier score, traffic lights approach, normal test and extended traffic lights approach. We introduce a modified extended traffic lights approach considering asset correlations.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.13-28
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• 2010

Assuming a mixture distribution for credit evaluation studies, we discuss estimating threshold methods to minimize errors that default borrowers are predicted as non defaults or non defaults are regarded as defaults. A method by using statistical hypotheses tests, the most powerful test and generalized likelihood ratio test, for the probability density functions which are defined with the score random variable and the parameter space consisted of only two elements such as the default and non default states is proposed to estimate a threshold. And anther optimal thresholds to maximize classification accuracy measures of the accuracy and the true rate for ROC and CAP curves are estimated as equations related with these probability density functions. Three kinds of optimal thresholds in terms of the hypotheses testing, the accuracy and the true rate are obtained from normal random samples with various means and variances. The sums of the type I and type II errors corresponding to each optimal threshold are obtained and compared. Finally we discuss about their efficiency and derive conclusions.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2001.06a
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• pp.359-368
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• 2001

본 연구에서는 부도예측용 인공신경망의 입력노드 선정을 위한 휴리스틱으로 연결강도분석 접근법을 제안한다. 연결강도분석은 학습이 끝난 인공신경망에서 입력노드와 은닉노드와 연결된 가중치의 절대값 즉, 연결강도를 분석하여 입력변수를 선정하는 접근법으로, 본 연구에서는 약체연결뉴론제거법, 강체연결뉴론선택법 그리고 이 두 기법을 통합한 통합 연결강도 모형을 제안하여 각각 의사결정 트리 및 다변량판별분석에 의해 선정된 입력변수를 이용한 인공신경망 모형과 예측율을 비교한다. 실험 결과 본 연구에서 제안하고 있는 방법론이 의사결정트리나 다다변량판별분석 기법 보다 높은 예측율을 보여 주었다. 특히 두 기법의 통합연결강도 모형의 경우에는 다른 단일 기법보다 높은 예측율을 보이고 있다.