Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year


Cite Score 2016: 0.33

SCImago Journal Rank (SJR) 2016: 0.346
Source Normalized Impact per Paper (SNIP) 2016: 0.167

Mathematical Citation Quotient (MCQ) 2016: 0.32

Online
ISSN
2196-7040
See all formats and pricing
More options …
Volume 34, Issue 1-2 (Jun 2017)

Issues

Company rating with support vector machines

Russ A. Moro
  • Corresponding author
  • Department of Economics and Finance, Brunel University London, Uxbridge UB8 3PH, United Kingdom
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Wolfgang K. Härdle
  • Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Spandauer Str. 1, 10178 Berlin, Germany
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Dorothea Schäfer
Published Online: 2017-04-13 | DOI: https://doi.org/10.1515/strm-2012-1141

Abstract

This paper proposes a rating methodology that is based on a non-linear classification method, a support vector machine, and a non-parametric isotonic regression for mapping rating scores into probabilities of default. We also propose a four data set model validation and training procedure that is more appropriate for credit rating data commonly characterised with cyclicality and panel features. Tests on representative data covering fifteen years of quarterly accounts and default events for 10,000 US listed companies confirm superiority of non-linear PD estimation. Our methodology demonstrates the ability to identify companies of diverse credit quality from Aaa to Caa–C.

Keywords: Bankruptcy; company rating; probability of default; support vector machines

MSC 2010: 62-07; 62G05; 62P05

References

  • [1]

    E. Altman, Financial ratios, discriminant analysis and the prediction of corporate bankruptcy, J. Finance 23 (1968), no. 4, 589–609. CrossrefGoogle Scholar

  • [2]

    E. Altman and A. Saunders, Credit risk measurement: Developments over the last 20 years, J. Banking Finance 21 (1998), no. 11–12, 1721–1742. Google Scholar

  • [3]

    R. E. Barlow, J. M. Bartholomew, J. M. Bremmer and H. D. Brunk, Statistical Inference Under Order Restrictions, John Wiley & Sons, New York, 1972. Google Scholar

  • [4]

    E. Carrizosa, A. Nogales-Gómez and D. R. Morales, Strongly agree or strongly disagree? Rating features in support vector machines, Inform. Sci. 329 (2016), 256–273. Google Scholar

  • [5]

    A. H. Chen, N. Ju, S. C. Mazumdar and A. Verma, Correlated default risks and bank regulations, J. Money Credit Banking 38 (2006), 375–398. Google Scholar

  • [6]

    C.-C. Chen and S.-T. Li, Credit rating with a monotonicity-constrained support vector machine model, Expert Syst. Appl. 41 (2014), no. 16, 7235–7247. Web of ScienceCrossrefGoogle Scholar

  • [7]

    W.-H. Chen and J.-Y. Shih, A study of Taiwan’s issuer credit rating systems using support vector machines, Expert Syst. Appl. 30 (2006), no. 3, 427–435. CrossrefGoogle Scholar

  • [8]

    J. de Leeuw, K. Hornik and P. Mair, Isotone optimization in R: Pool-adjacent-violators algorithm (PAVA) and active set methods, J. Stat. Softw. 32 (2009), no. 5, 1–24. Google Scholar

  • [9]

    J.-C. Duan, J. Sun and T. Wang, Multiperiod corporate default prediction – A forward intensity approach, J. Econometrics 170 (2012), no. 1, 191–209. Web of ScienceGoogle Scholar

  • [10]

    D. W. Dwyer, A. E. Kocagil and R. M. Stein, Moody’s KMV RiskCalc v3.1 model: Next-generation technology for predicting private firm credit risk, White Paper (2004), Moody’s KMV Company. Google Scholar

  • [11]

    B. Engelmann, E. Hayden and D. Tasche, Measuring the discriminative power of rating systems, Discussion Paper Series 2: Banking and Financial Supervision, Deutsche Bundesbank, 2003. Google Scholar

  • [12]

    E. Falkenstein, A. Boral and L. Carty, Riskcalc for private companies: Moody’s default model, Report 56402, Moody’s Investors Service, New York, 2000. Google Scholar

  • [13]

    J. E. Fernandes, Corporate credit risk modeling: Quantitative rating system and probability of default estimation, preprint (2005), http://econwpa.repec.org/eps/fin/papers/0505/0505013.pdf.

  • [14]

    T. V. Gestel, J. A. K. Suykens, G. Lanckriet, A. Lambrechts, B. D. Moor and J. Vandewalle, Bayesian framework for least-squares support vector machine classifiers, Gaussian processes, and kernel Fisher discriminant analysis, J. Neural Comput. 14 (2002), no. 5, 1115–1147. CrossrefGoogle Scholar

  • [15]

    D. Glennon and P. Nigro, Measuring the default risk of small business loans: A survival analysis approach, J. Money Credit Banking 37 (2005), no. 5, 923–947. Google Scholar

  • [16]

    S. J. Grotzinger and C. Witzgall, Projections onto simplices, Appl. Math. Optim. 12 (1984), no. 1, 247–270. CrossrefGoogle Scholar

  • [17]

    P. Hajek and K. Michalak, Feature selection in corporate credit rating prediction, Knowledge Based Syst. 51 (2013), 72–84. Google Scholar

  • [18]

    D. T. Hamilton and R. Cantor, Measuring corporate default rates, Report 100779, Moody’s Investors Service, 2006. Google Scholar

  • [19]

    D. Hand, Measuring classifier performance: A coherent alternative to the area under the ROC curve, Mach. Learn. 77 (2009), no. 1, 103–123. Google Scholar

  • [20]

    J. A. Hanley and B. J. McNeil, The meaning and use of the area under a receiver operating characteristic (ROC) curve, Radiology 143 (1982), no. 1, 29–36. Google Scholar

  • [21]

    Z. Huang, H. Chen, C.-J. Hsu, W.-H. Chen and S. Wu, Credit rating analysis with support vector machines and neural networks: A market comparative study, Decis. Support Syst. 37 (2004), no. 4, 543–558. CrossrefGoogle Scholar

  • [22]

    A. Karatzoglou, D. Meyer and K. Hornik, Support vector machines in R, J. Stat. Softw. 15 (2006), no. 9, 1–28. Google Scholar

  • [23]

    K. Kim and H. Ahn, A corporate credit rating model using multi-class support vector machines with an ordinal pairwise partitioning approach, Comput. Oper. Res. 39 (2012), no. 8, 1800–1811. Google Scholar

  • [24]

    J. T.-Y. Kwok, Moderating the outputs of support vector machine classifiers, IEEE Trans. Neural Networks 10 (1999), no. 5, 1018–1031. CrossrefGoogle Scholar

  • [25]

    J. T.-Y. Kwok, The evidence framework applied to support vector machines, IEEE Trans. Neural Networks 11 (2000), no. 5, 1162–1173. CrossrefGoogle Scholar

  • [26]

    Y.-C. Lee, Application of support vector machines to corporate credit rating prediction, Expert Syst. Appl. 33 (2007), no. 1, 67–74. Web of ScienceCrossrefGoogle Scholar

  • [27]

    H. B. Mann and D. R. Whitney, On a test of whether one of two random variables is stochastically larger than the other, Ann. Math. Stat. 18 (1947), no. 1, 50–60. CrossrefGoogle Scholar

  • [28]

    M. J. Manning, Exploring the relationship between credit spreads and default probabilities, Working Paper 225, Bank of England, 2004. Google Scholar

  • [29]

    D. Martens, B. Baesens, T. van Gestel and J. Vanthienen, Comprehensible credit scoring models using rule extraction from support vector machines, Working Paper 878283, Social Science Research Network, 2006. Google Scholar

  • [30]

    D. Martin, Early warning of bank failure: A logit regression approach, J. Banking Finance 1 (1977), no. 3, 249–276. CrossrefGoogle Scholar

  • [31]

    R. C. Merton, On the pricing of corporate debt: The risk structure of interest rates, J. Finance 29 (1974), no. 2, 449–470. Google Scholar

  • [32]

    J. A. Ohlson, Financial ratios and the probabilistic prediction of bankruptcy, J. Accounting Res. 18 (1980), no. 1, 109–131. CrossrefGoogle Scholar

  • [33]

    J. C. Platt, Probabilities for SV machines, Advances in Large Margin Classifiers, The MIT Press, Cambridge (2000), 61–73. Google Scholar

  • [34]

    M. D. Richard and R. P. Lippmann, Neural network classifiers estimate Bayesian a posteriori probabilities, J. Neural Comput. 3 (1991), no. 4, 461–483. CrossrefGoogle Scholar

  • [35]

    B. Schölkopf and A. J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, London, 2002. Google Scholar

  • [36]

    W. Sjur, S. Hol and N. van der Wijst, Capital structure, business risk, and default probability, Discussion Paper 975302, Social Science Research Network, 2007. Google Scholar

  • [37]

    V. M. Tikhomirov, The evolution of methods of convex optimization, Amer. Math. Monthly 103 (1996), no. 1, 65–71. CrossrefGoogle Scholar

  • [38]

    V. Vapnik, The Nature of Statistical Learning Theory, Springer, New York, 1995. Google Scholar

  • [39]

    L. Yu, X. Yao, S. Wang and K. K. Lai, Credit risk evaluation using a weighted least squares svm classifier with design of experiment for parameter selection, Expert Syst. Appl. 12 (2011), 15392–15399. Web of ScienceCrossrefGoogle Scholar

About the article

Received: 2012-10-18

Revised: 2016-12-01

Accepted: 2017-03-02

Published Online: 2017-04-13

Published in Print: 2017-06-01


Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: SFB 649 “Economic Risk”

The authors gratefully acknowledge the support of this project by the Risk Management Institute of the National University of Singapore (RMI NUS). We thank RMI NUS for providing access to their database of financial statements and default events. Russ A. Moro was financially supported by the RMI NUS and Wolfgang K. Härdle by Deutsche Forschungsgemeinschaft through SFB 649 “Economic Risk”.


Citation Information: Statistics & Risk Modeling, ISSN (Online) 2196-7040, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1515/strm-2012-1141.

Export Citation

© 2017 Walter de Gruyter GmbH, Berlin/Boston. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in