Modeling default risk via a hidden Markov model of multiple sequences

doi:10.1007/s11704-010-0501-9

Front Comput Sci Chin

0, Vol.

Issue () : 187-195 https://doi.org/10.1007/s11704-010-0501-9

Modeling default risk via a hidden Markov model of multiple sequences

Wai-Ki CHING¹(

), Ho-Yin LEUNG¹(

), Zhenyu WU²(

), Hao JIANG¹(

)

1. Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Hong Kong, China; 2. Department of Finance and Management Science, N. Murray Edwards School of Business, University of Saskatchewan, Saskatoon, SK S7N 5A7, Canada

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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

Corresponding Author(s): CHING Wai-Ki,Email:wching@hkusua.hku.hk; LEUNG Ho-Yin,Email:obliging@hkusua.hku.hk; WU Zhenyu,Email:wu@edwards.usask.ca; JIANG Hao,Email:jianghao191@163.com

Issue Date: 05 June 2010

Cite this article:

Ho-Yin LEUNG,Wai-Ki CHING,Zhenyu WU, et al. Modeling default risk via a hidden Markov model of multiple sequences[J]. Front Comput Sci Chin, 0, (): 187-195.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-010-0501-9
https://academic.hep.com.cn/fcs/EN/Y0/V/I/187

Fig.1 Hidden sequence of “0’’ and “1’’ inferred by MHMM in different quarters

Fig.2 Hidden sequence of “0’’ and “1’’ inferred by HMM in different quarters. (a) Consumer; (b) Energy; (c) Media; (d) Transportation

Tab.1 Default probability of a bond in MHMM

Tab.2 Default probability of a bond in HMM

Tab.3 VaR and ES in MHMM and HMM at the 95% significance level

Tab.4 VaR and ES in MHMM and HMM at the 99% significance level

Fig.3 Prediction probability of the real risk state for different quarters. Circle represents prediction probability

Fig.4 Prediction accuracy for different (a) Unbalanced; (b) balanced

Fig.5 Prediction errors for different . (a) Type A; (b) Type B

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