Analysis of default data using hidden Markov models

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.