Information theoretic generator estimation with an application to ratings process migration

The characterisation of obligor ratings dynamics as a Markov chain is a common assumption in credit risk modelling. While a continuous time Markov chain is most appealing on account of the potential for more robust transition probability estimates, the cost of continuously monitoring obligor ratings can be too high to justify the assumption in practice. Linking the discrete and continuous Markov chains is a generator matrix that allows for the determination of transition probabilities for any timescale of interest. Known as the embeddability problem, empirical transition probability estimates for ratings processes rarely possess an exact generator suggesting that methods for finding a generator matrix comprise an important area of research. In this paper, an econometric model for estimating generator intensities is suggested that is flexible, non-parametric and does not rely on previously estimated transition probabilities.