Modeling default risk via a hidden Markov model of multiple sequences

Wai-Ki CHING, Ho-Yin LEUNG, Zhenyu WU, Hao JIANG

Front. Comput. Sci. ›› 0

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PDF(273 KB)
Front. Comput. Sci. ›› DOI: 10.1007/s11704-010-0501-9
RESEARCH ARTICLE

Modeling default risk via a hidden Markov model of multiple sequences

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Abstract

Default risk in commercial lending is one of the major concerns of the creditors. In this article, we introduce a new hidden Markov model (HMM) with multiple observable sequences (MHMM), assuming that all the observable sequences are driven by a common hidden sequence, and utilize it to analyze default data in a network of sectors. Efficient estimation method is then adopted to estimate the model parameters. To further illustrate the advantages of MHMM, we compare the hidden risk state process obtained by MHMM with that from the traditional HMMs using credit default data. We then consider two applications of our MHMM. The calculation of two important risk measures: Value-at-risk (VaR) and expected shortfall (ES) and the prediction of global risk state. We first compare the performance of MHMM and HMM in the calculation of VaR and ES in a portfolio of default-prone bonds. A logistic regression model is then considered for the prediction of global economic risk using our MHMM with default data. Numerical results indicate our model is effective for both applications.

Keywords

bond / default / hidden Markov model (HMM) / value-at-risk (VaR) / expected shortfall (ES) / logistic regression model / prediction

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Wai-Ki CHING, Ho-Yin LEUNG, Zhenyu WU, Hao JIANG. Modeling default risk via a hidden Markov model of multiple sequences. Front Comput Sci Chin, https://doi.org/10.1007/s11704-010-0501-9

References

[1]
Li D. On default correlation: a Copula function approach. Journal of Fixed Income, 2000, 9(4): 43-54
CrossRef Google scholar
[2]
McNeil A, Frey R, Embrechts P. Quantitative risk management: concepts, techniques and tools. Princeton University Press, 2005
[3]
Credit Suisse Financial Products. Credit Risk+ a Credit Risk Management Framework, 1997, http://www.csfb.com/institutional/research/creditrisk.html
[4]
Duffie D, Eckner A, Horel G, Saita L. Frailty correlated default, Graduate School of Business, Stanford University, 2006, Preprint
[5]
Das S, Duffie D, Kapadia N, Saita L. Common failings: how corporate defaults are correlated? Journal of Finance, 2007, 62(1): 93-117
CrossRef Google scholar
[6]
Moody’s Investment Services. The Binomial Expansion Method Applied to CBO/CLO Analysis. 1999
[7]
Davis M, Lo V. Infectious defaults. Quantitative Finance, 2001, 1(4): 382-387
CrossRef Google scholar
[8]
Davis M, Lo V. Modeling default correlation in bond portfolio. In: Alescander C, ed. Mastering Risk Volume 2: Applications. Financial Times, Prentice Hall, 2001, 141-151
[9]
Giampieri G, Davis M, Crowder M. Analysis of default data using hidden Markov models. Quantitative Finance, 2005, 5(1): 27-34
CrossRef Google scholar
[10]
MacDonald I, Zucchini W. Hidden Markov and Other Models for Discrete-Valued Time Series. London:. Chapman & Hall, 1999
[11]
Rabiner L R. A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE, 1989, 77(2): 257-286
CrossRef Google scholar
[12]
Ching W, Ng M. Markov Chains: Models, Algorithms and Applications. International Series on Operations Research and Management Science, New York: Springer, 2006
[13]
Ching W, Ng M, Wong K. Hidden Markov models and thier applications to customer relationship management. IMA Journal of Management Mathematics, 2004, 15(1): 13-24
CrossRef Google scholar
[14]
Ching W, Fung E, Ng M, Siu T, Li W. Interactive hidden Markov models and their applications. IMA Journal of Management Mathematics, 2007, 18(1): 85-97
CrossRef Google scholar
[15]
Ching W, Siu T, Li L, Li T, Li W. Modeling default data via an interactive hidden Markov model, Computational Economics. Computational Economics, 2009, 34(1): 1-19
CrossRef Google scholar
[16]
Ching W K, Leung H, Jiang H, Wu Z. Hidden Markov models for default risk. In: Proceedings of the 2nd International Symposium on Financial Information Processing (FIP), Beijing, China, 2009
[17]
Levinson S, Rabiner L, Sondhi M. An introduction to the application if theory of probabilistic functions of Markov process to automatic speech recognition. Bell System Technical Journal, 1983, 62: 1035-1074
[18]
Li X, Parizeau M, Plamondon R. Training hidden Markov models with multiple observation- a combinatorial method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(4): 371-377
CrossRef Google scholar
[19]
Zhang D, Shi Y, Tian Y, Zhu M. A class of classification and regression methods by multiobjective programming. Frontiers of Computer Science in China, 2009, 3(2): 192-204
CrossRef Google scholar
[20]
Zhou L, Lai K. Benchmarking binary classification models on data sets with different degrees of imbalance. Frontiers of Computer Science in China, 2009, 3(2): 205-216
CrossRef Google scholar
[21]
Richard A, Johnson, Dean W. Wichern. Applied Multivariate Statistical Analysis. Prentice Hall International Series, U.S. 1992, 553
[22]
Siu T K, Ching W K, Fung E S, Ng M K. Extracting information from spot interest rates and credit ratings using double higher-order hidden Markov models. Computational Economics, 2005, 26(3): 69-102
CrossRef Google scholar

Acknowledgements

A preliminary version of the paper was presented in the 2nd International Symposium on Financial Information Processing (FIP) [22]. Research supported in part by RGC Grants 7017/07P and HKU Strategic Research Theme Fund on Computational Sciences and Hung Hing Ying Physical Sciences Research Fund.

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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