Computational Economics

, Volume 34, Issue 1, pp 1–19 | Cite as

Modeling Default Data Via an Interactive Hidden Markov Model

  • Wai-Ki Ching
  • Tak Kuen SiuEmail author
  • Li-min Li
  • Tang Li
  • Wai-Keung Li


In this paper, we first introduce the use of an interactive hidden Markov model (IHMM) for modeling and analyzing default data in a sector. Under the IHMM, transitions of the hidden risk states of the sector depend on the observed number of bonds in the sector that default in the current time period. This incorporates the feedback effect of the number of defaults on the transitions of the hidden risk states. This feature seems to be more realistic and does not enjoy by the traditional HMMs. We then develop a “dynamic” version of the binomial expansion technique (BET) modulated by the IHMM for modeling the occurrence of defaults of bonds issued by firms in the same sector. Under the BET modulated by the IHMM, the number of bonds defaulting in each time period follows a Markov-modulated binomial distribution with the probability of defaulting of each bond depending on the states of the IHMM, which represent the hidden risk states of the sector. Efficient method will be presented for estimating the model parameters in the BET modulated by the IHMM. We shall compare the hidden risk state process extracted from the IHMM-modulated BET with that extracted from the BET modulated by HMM in order to illustrate the significance of the feedback effect using real data. We shall also present the estimation results for the BET modulated by the IHMM and compare them with those for the BET modulated by the HMM.


Default data Hidden Markov model (HMM) Interactive hidden Markov model (IHMM) Binomial expansion technique Feedback effect 


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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Wai-Ki Ching
    • 1
  • Tak Kuen Siu
    • 2
    Email author
  • Li-min Li
    • 1
  • Tang Li
    • 1
  • Wai-Keung Li
    • 3
  1. 1.Advanced Modeling and Applied Computing Laboratory, Department of MathematicsThe University of Hong KongHong KongChina
  2. 2.Department of Actuarial Studies, Faculty of Business and EconomicsMacquarie UniversitySydneyAustralia
  3. 3.Department of Statistics and Actuarial ScienceThe University of Hong KongHong KongChina

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