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Shiu Fung Wong

First Name: Shiu Fung
Surname: Wong
Department Dept of Applied Finance and Actuarial Studies
Supervisor(s): Tak Kuen Siu , Robert Elliott

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Paper Title

Filtering a Hidden Markov-Modulated Intensity-Based Credit Risk Model


To use an intensity-based model for portfolio credit risk using a collection of hidden Markov-modulated single jump processes.


The default observations are single jump processes which contain very limited information. This is the first filtering scheme which provides practical implementation and results.

Key literature/theoretical perspective

The proposed model adopts a frailty-based approach to describe the dependent default risk, where firms are exposed to a common unobservable factor, namely, a frailty factor. We model this frailty factor by another continuous-time, finite-state, hidden Markov chain.


A (robust) filter for the frailty factor is derived and a corresponding (robust) filter-based EM algorithm for the recursive estimates of unknown parameters is developed. We also evaluate the joint default probability of entities in a credit portfolio in the proposed model. Using the joint characteristic function of the occupation times of the chain and the inverse Fourier transform, a (semi)-analytical formula for the joint default probability of the constituents in the credit portfolio is derived, which can be evaluated based on observed default information.


Hidden Markov-modulated model parameters, default intensities and filtered hidden Markov states are estimated in very high accuracy from limited information in the single-jump processes.


Intensity-Based Credit Model; Hidden Markov Chain; Frailty Model; Robust Filters; Joint Default Probability.