A corporate credit rating model using multi-class support vector machines with an ordinal pairwise partitioning approach☆
Introduction
Corporate credit rating is a very important factor in the market of corporate debt. Information concerning corporate operations is often disseminated to market participants through the changes in credit ratings that are published by professional rating agencies, such as Standard & Poor's (S&P) and Moody's Investor Service. Since these agencies generally require large fees for their services and the periodically provided ratings sometimes do not reflect the default risk of the company at the time, it may be advantageous for bond-market participants to be able to classify credit ratings before the agencies publish the ratings. As a result, it is very important for the companies, especially financial companies, to develop a proper model of credit rating [1], [68].
From a technical perspective, the credit rating constitutes a typical, multi-class, classification problem because the rating agencies generally have ten or more categories of ratings. For example, S&P's ratings range from AAA for the highest-quality bonds to D for the lowest-quality bonds. Professional rating agencies emphasize the importance of analysts' subjective judgments in determining credit ratings. However, in practice, a mathematical model that uses the financial variables of companies plays an important role in determining credit ratings, since it is convenient to apply and entails less time and cost. These financial variables include the ratios that represent a company's leverage status, liquidity status, and profitability status [1], [2], [3], [4], [68], [69].
Several statistical and artificial intelligence (AI) techniques have been applied as tools for financial decision making such as stock market forecasting or credit ratings prediction [1], [3], [5]. Among them, the artificial neural networks have been widely used in the area of finance because of their broad applicability to many business problems and their preeminent ability to learn [6], [7]. However, besides the risk of over-fitting, artificial neural networks also have many defects, including difficulty in determining the values of control parameters and the number of processing elements in the layer. Support vector machines (SVMs) have recently become popular as a solution to problems that are associated with prediction because of their robustness and high accuracy [8], [9], [10], [11], [12], [70]. An SVM's solution may be globally optimal because SVMs seek to minimize structural risk. Conversely, the solutions found by artificial neural network models tend to fall into local optimum because they seek to minimize empirical risk. In addition, no parameters need to be tuned in SVMs, barring the upper bound for non-separable cases in linear SVMs. However, SVMs were originally devised for binary classification; therefore, they are not naturally geared for multi-class classifications, which apply to credit ratings [13]. Thus, researchers have tried to extend the original SVM to multi-class classification.
Hitherto, a variety of techniques to extend standard SVMs to multi-class SVMs (MSVMs) have been proposed in the literature. These techniques include approaches that construct and combine several binary classifiers as well as approaches that directly consider all the data in a single optimization formulation. However, most published techniques have focused on classifying samples into nominal categories [8], [14], [15], [16], [17], [18], [19], [20], [21]. Even those prior studies that applied MSVMs to credit ratings also used standard MSVM models that were not designed to reflect the ordinal nature of this domain [1], [3], [22], [23]. Furthermore, most of these studies tested at most a few types of MSVM.
In this study, we propose a novel computational approach for MSVMs, which takes into account the ordinal characteristics for efficiently and effectively handling multiple ordinal classes; we term the approach, ordinal multi-class support vector machine (or OMSVM, in short). Similar to traditional MSVMs, our model basically combines several binary SVM classifiers. However, it is different from the traditional approaches since it extends the binary SVMs using the ordinal pairwise partitioning (OPP) approach [24]. Using the latter approach, our model uses fewer classifiers, but nevertheless may more accurately predict classes because it exploits additional hidden information, namely, the order of classes. To validate the effectiveness of our model, we applied the model to a real-world case of bond rating in Korea. We compared the results of the model to those of traditional MSVM approaches. We also compared the results of the model to those of traditional techniques for credit ratings, such as multiple discriminant analysis (MDA), multinomial logistic regression (MLOGIT), case-based reasoning (CBR), and artificial neural networks (ANNs) [25], [26], [27], [28], [29], [30], [31], [32], [33]. In addition, to examine the effect of OPP in depth, we applied OPP to both MSVMs and ANNs, and we compared the prediction results that were generated by these two techniques.
The rest of this paper is organized as follows. The next section reviews the literature on SVMs and MSVMs, in addition to studies on credit ratings that employed data mining. In Section 3, our approach for ordinal multi-class classification is proposed. Section 4 describes the data and experiments for validating our model. In Section 5, the empirical results are summarized and discussed. The final section presents the conclusions and future research direction of this study.
Section snippets
Literature review
In this section, we introduce the basic concept of conventional SVM, and we summarize the studies that have attempted to extend the conventional SVM to multi-class classification. Then, we briefly review the studies on credit ratings that have used the techniques of data mining. We will also discuss the major studies in the literature that have adopted MSVMs to classify credit ratings.
A novel approach of MSVMs for credit rating: OMSVM
As mentioned in the previous section, MSVMs have recently been receiving attention from researchers, who investigate achieving effective and efficient classifiers for credit ratings. Several articles that validate the applicability of MSVMs to the credit-rating domain have already been published. However, it is worth noting that most of these studies have merely adopted those MSVM techniques that had been developed by other researchers, without any modification or improvement. Furthermore, the
Research data
To validate our model, we applied it to a real-world case of credit rating in Korea. Our application is in bond rating, which is the most frequently studied area of credit rating for specific debt issues or other financial obligations. The research data were collected from National Information and Credit Evaluation, Inc., a major bond-rating company in Korea. We obtained the bond-ratings for the year 2002 and various financial variables for 1295 companies from the manufacturing industry in
Experimental results
To compare the performance of each algorithm, we adopted the hit-ratio as the performance measure. Simply put, the hit-ratio means the ratio of the corrected cases over all cases. The ratio is defined in
In Eq. (10), CR is the classification accuracy rate of the test-set, CAi is the classification accuracy of the ith case of the test-set denoted by either 1 or 0 (‘correct’=1, ‘incorrect’=0), POi is the predicted outcome for the ith case, and AOi is the
Conclusions and directions for future research
In this study, we proposed a novel MSVM algorithm that was optimized for credit rating. In contrast to prior studies that just applied conventional MSVMs to credit ratings, we suggested a new MSVM algorithm, called OMSVM, which is designed to use order-information in ordinal multi-class classification problems. To validate the applicability of the proposed algorithm, we applied it to a real case of bond rating. As a result, we found that OMSVM outperformed many kinds of MSVM approaches proposed
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This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2009-332-B00104). This work was supported by the 2011 research fund of Kookmin University in Korea.