Credit spread approximation and improvement using random forest regression. (English) Zbl 1431.91415

Summary: Credit default swap (CDS) levels provide a market appreciation of companies’ default risk. These derivatives are not always available, creating a need for CDS approximations. This paper offers a simple, global and transparent CDS structural approximation, which contrasts with more complex and proprietary approximations currently in use. This equity-to-credit formula (E2C), inspired by CreditGrades, obtains better CDS approximations, according to empirical analyses based on a large sample spanning 2016-2018. A random forest regression run with this E2C formula and selected additional financial data results in an 87.3% out-of-sample accuracy in CDS approximations. The transparency property of this algorithm confirms the predominance of the E2C estimate, and the impact of companies’ debt rating and size, in predicting their CDS.


91G40 Credit risk
91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI arXiv


[1] Ahmad, M. W.; Mourshed, M.; Rezgui, Y., Trees vs neurons: Comparison between random forest and ann for high-resolution prediction of building energy consumption, Energy and Buildings, 147, 77-89, (2017)
[2] Ando, T., Bayesian corporate bond pricing and credit default swap premium models for deriving default probabilities and recovery rates, Journal of the Operational Research Society, 65, 454-465, (2014)
[3] Badrinarayanan, V.; Kendall, A.; Cipolla, R., SegNet: A deep convolutional encoder-decoder architecture for image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 39, 2481-2495, (2017)
[4] Basak, S.; Kar, S.; Saha, S.; Khaidem, L.; Roy Dey, S., Predicting the direction of stock market prices using tree-based classifiers, The North American Journal of Economics and Finance, 47, 552-567, (2019)
[5] Behr, A.; Weinblat, J., Default patterns in seven eu countries: A random forest approach, International Journal of the Economics of Business, 24, 2, 181, (2017)
[6] Black, F.; Cox, J., Valuing corporate securities: Some effects of bond indenture provisions, Journal of Finance, 31, 351-367, (1976)
[7] Breiman, L., Bagging predictors, Machine Learning, 24, 123-140, (1996) · Zbl 0858.68080
[8] Breiman, L., Random forests, Machine Learning, 45, 5-32, (2001) · Zbl 1007.68152
[9] Breiman, L.; Friedman, J.; Stone, C. J.; Olshen, R. A., Classification and regression trees, (1984), Wadsworth and Brooks · Zbl 0541.62042
[10] Brummelhuis, R.; Luo, Z., CDS rate construction methods by machine learning techniques, Presentation at invitation by Department of Statistics at London School of Economics (March 7, 2017), 1-51, (2017), SSRN Journals: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2967184
[11] Chalamandaris, G.; Vlachogiannakis, N., Are financial ratios relevant for trading credit risk? evidence from the CDS market, Annals of Operations Research, 266, 395-440, (2018) · Zbl 1404.62102
[12] Chebyshev, P. L., Des valeurs moyennes, Journal de mathématiques pures et appliquées, 12, 177-184, (1867)
[13] Cont, R.; Minca, A., Credit default swaps and systemic risk, Annals of Operations Research, 247, 523-547, (2016) · Zbl 1406.91471
[14] Eom, Y. H.; Helwege, J.; Huang, J.-Z., Structural models of corporate bond pricing: An empirical analysis, The Review of Financial Studies, 17, 499-544, (2004)
[15] Escobar, M.; Arian, H.; Seco, L., Creditgrades framework within stochastic covariance models, Journal of Mathematical Finance, 2, 303-314, (2012)
[16] Fernandez-Delgado, M.; Cernadas, E.; Barro, S.; Amorim, D., Do we need hundreds of classifiers to solve real world classification problems?, Journal of Machine Learning Research, 15, 3133-3181, (2014) · Zbl 1319.62005
[17] Finger, C. C.; Lardy, J. P.; Finkelstein, V.; Pan, G.; Ta, T.; Tierney, J., CreditGrades, Technical Report, (2002), RiskMetrics Group
[18] Python Software Foundation (2016). Python 3.6.0 documentation. https://docs.python.org/3.6/.
[19] Friedman, J. H., Greedy function approximation: A gradient boosting machine, The Annals of Statistics, 29, 5, 1189-1232, (2001) · Zbl 1043.62034
[20] Gauss, C. F., Theoria combinationis observationum erroribus minimus obnoxiae (pars prior), 4, 3-26, (1821)
[21] Guarin, A.; Liu, X.; Ng, W. L., Enhancing credit default swap valuation with meshfree methods, European Journal of Operational Research, 214, 805-813, (2011) · Zbl 1219.91139
[22] Hastie, T.; Tibshirani, R.; Friedman, J., The elements of statistical learning, (2009), Springer Series in Statistics
[23] Ho, T. K., Random decision forests, Proceedings of the third international conference on document analysis and recognition, 278-282, (1995)
[24] Ho, T. K., The random subspace method for constructing decision forests, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, 832-844, (1998)
[25] Hunter, J.; Dale, D., The matplotlib users guide, Technical Report, (2007), R Cran
[26] Imbierowicz, B.; Cserna, B., How efficient are credit default swap markets? an empirical study of capital structure arbitrage based on structural pricing model, 21st Australasian Finance and Banking Conference 2008 Paper, (2008), SSRN Journals: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1099456
[27] Irresberger, F.; Weiss, G.; Gabrysch, J.; Gabrysch, S., Liquidity tail risk and credit default swap spreads, European Journal of Operational Research, 269, 1137-1153, (2018) · Zbl 1390.91313
[28] Koutmos, D., Interdependencies between CDS spreads in the european union: Is greece the black sheep or black swan?, Annals of Operations Research, 266, 441-498, (2018) · Zbl 1404.62142
[29] Krauss, C.; Do, X. A.; Huck, N., Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500, European Journal of Operational Research, 259, 689-702, (2017) · Zbl 1395.91514
[30] Lardic, S.; Rouzeau, E., Implementing Merton’s model on the french corporate bond market, Proceedings of the AFFI conference, (1999)
[31] LeCun, Y. (2012). Learning invariant feature hierarchies. Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics) Computer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings. Part 1 ed. Vol. 7583 LNCS. p. 496-505.
[32] Lévy, P., Sur certains processus stochastiques homogènes, Compositio Mathematica, 7, 283-339, (1940) · JFM 65.1346.02
[33] Liaw, A.; Wiener, M., Classification and regression by randomforest, R News, 2, 3, 18-22, (2002)
[34] Liu, M.; Wang, M.; Wang, J.; Li, D., Comparison of random forest, support vector machine and back propagation neural network for electronic tongue data classification: Application to the recognition of orange beverage and chinese vinegar, Sensors and Actuators B: Chemical, 177, 970-980, (2013)
[35] McKinney, W., Data structures for statistical computing in python, Proceedings of the ninth Python in science conference, 445, 51-56, (2010)
[36] Merton, R., On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance, 29, 449-470, (1974)
[37] Nyman, R., & Ormerod, P. (2016). Predicting economic recessions using machine learning algorithms. Cornell University Library (Working Paper) January. arxiv:1701.01428.
[38] Opitz, D.; Maclin, R., Popular ensemble methods: An empirical study, Journal of Artificial Intelligence Research, 11, 169-198, (1999) · Zbl 0924.68159
[39] Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O., Scikit-learn: Machine learning in python, Journal of Machine Learning Research, 12, 2825-2830, (2011) · Zbl 1280.68189
[40] Perks, W., A simple proof of Gauss’s inequality, Journal of the Staple Inn Actuarial Society, 7, 1, 38-41, (1947)
[41] Rodrigues, M., & Agarwal, V. (2011). The performance of structural models in pricing credit spreads. Midwest Finance Association 2012 Annual Meetings Paper, (pp. 1-26). SSRN Journals: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1929177.
[42] Rodriguez-Galiano, V.; Sanchez-Castillo, M.; Chica-Olmo, M.; Chica-Rivas, M., Machine learning predictive models for mineral prospectivity: An evaluation of neural networks, random forest, regression trees and support vector machines, Ore Geology Reviews, 71, 804-818, (2015)
[43] Roy, A. D., Safety first and the holding of assets, Econometrica, 20, 431-449, (1952) · Zbl 0047.38805
[44] Sangineto, E.; Nabi, M.; Culibrk, D.; Sebe, N., Self paced deep learning for weakly supervised object detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, PP, 1-10, (2018)
[45] Santos, K. (2008). Corporate credit ratings: a quick guide. https://www.treasurers.org/ACTmedia/ITCCMFcorpcreditguide.pdf.
[46] Schönbucher, P. J., Credit derivatives pricing models, (2003), Wiley Finance
[47] Sepp, A., Extended CreditGrades model with stochastic volatility and jumps, Wilmott Magazine, 50-62, (2006)
[48] Shwartz-Ziv, R.; Tishby, N., Opening the black box of deep neural networks via information, (2017), arxiv: 1703.00810
[49] Stamicar, R.; Finger, C. C., Incorporating equity derivatives into the creditgrades model, Journal of Credit Risk, 2, 1, 3-29, (2006)
[50] StataCorp (2013). Stata 13. https://www.stata.com/stata13/.
[51] Sun, Y.; Yen, G. G.; Yi, Z., Evolving unsupervised deep neural networks for learning meaningful representations, IEEE Transactions on Evolutionary Computation, PP, 1-10, (2018)
[52] Tanaka, K.; Kinkyo, T.; Hamori, S., Random forests-based early warning system for bank failures, Economics Letters, 148, 118-121, (2016)
[53] Teixeira, J. C.A., An empirical analysis of structural models of corporate debt pricing, Applied Financial Economics, 17, 14, 1141-1165, (2007)
[54] Vasicek, O. A., Probability of loss on loan portfolio, (1987), KMV Corporation
[55] Walt, S. V.D.; Colbert, S.; Varoquaux, G., The numpy array: a structure for efficient numerical computation, Computing in Science & Engineering, 13, 22-30, (2011)
[56] Yeh, C. C.; Lin, F.; Hsu, C. Y., A hybrid KMV model, random forests and rough set theory approach for credit rating, Knowledge-Based Systems, 33, 166-172, (2012)
[57] Zhou, C., A jump-diffusion approach to modeling credit risk and valuing defaultable securities, Finance and economics discussion papers 1997/15, (1997)
[58] Zhou, C., An analysis of default correlations and multiple defaults, Review of Financial Studies, 14, 2, 555-576, (2001)
[59] Zhou, C., The term structure of credit spreads with jump risk, Journal of Banking & Finance, 25, 2015-2040, (2001)
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