zbMATH — the first resource for mathematics

Analysis of default data using hidden Markov models. (English) Zbl 1118.91321
Summary: The occurrence of defaults within a bond portfolio is modelled as a simple hidden Markov process. The hidden variable represents the risk state, which is assumed to be common to all bonds within one particular sector and region. After describing the model and recalling the basic properties of hidden Markov chains, we show how to apply the model to a simulated sequence of default events. Then, we consider a real scenario, with default events taken from a large database provided by Standard & Poor’s. We are able to obtain estimates for the model parameters and also to reconstruct the most likely sequence of the risk state. Finally, we address the issue of global versus industry-specific risk factors. By extending our model to include independent hidden risk sequences, we can disentangle the risk associated with the business cycle from that specific to the individual sector.

91B28 Finance etc. (MSC2000)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
PDF BibTeX Cite
Full Text: DOI
[1] CreditRisk+ a credit risk management framework (1997)
[2] DOI: 10.1080/713665832
[3] Davis M, Mastering Risk Volume 2: Applications pp pp. 141–151– (2001)
[4] Duffie D, Credit Risk: Pricing, Measurement and Management (2003)
[5] Frey R, Working Paper (2004)
[6] Frey R, J. Risk 6 pp 59– (2003)
[7] Giesecke K, J. Econ. Dynamics Control
[8] DOI: 10.1016/j.jbankfin.2003.11.002
[9] DOI: 10.1111/0022-1082.00389
[10] DOI: 10.3905/jfi.2000.319253
[11] MacDonald IL, Hidden Markov and Other Models for Discrete-valued Time Series (1997) · Zbl 0868.60036
[12] DOI: 10.2307/2978814
[13] Technical document (1997)
[14] US business cycle expansions and contractions (2003)
[15] Technical document (1997)
[16] Schönbucher P, Credit Derivatives Pricing Models (2003)
[17] Vasicek O, Working Paper (1987)
[18] Vasicek O Limiting loan loss probability distribution 1991 (Moody’s KMV)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.