Interacting default intensity with a hidden Markov process

Abstract

In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method can be applied to a wide range of problems. Based on this model, we derive the joint distribution of multiple default times without imposing stringent assumptions on the form of default intensities. Closed-form formulas for the distribution of default times are obtained which are then applied to solve a number of practical problems such as hedging and pricing credit derivatives. The method and numerical algorithms presented can be applicable to various forms of default intensities.

Keywords:

• Reduced-form intensity model
• Default risk
• Credit derivatives
• Hidden Markov model (HMM)

Acknowledgements

The authors would like to thank the two anonymous referees and the editor for their helpful comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research work was supported by Research Grants Council of Hong Kong [grant number 17301214]; HKU CERG Grants and HKU Strategic Research Theme in Information and Computing.