Decomposing Rating Migration Matrices from Market Prices Revisited

Abstract

The study revisits the method and premises of decomposing rating migration matrices from price data. Default and non-default probability term structures are first decomposed from market prices. This represents the composite default probability structure or process of a rating category, when considering rating migration and future ratings probabilities. A rating migration matrix is subsequently decomposed from this output. Output residuals are low, yet the optimization problem finds many local solutions, rather than a solid global solution: different rating migration matrices can result in and produce the same decomposed default probability term structures. Price data contain sufficient information to decompose the default and non-default probability term structures, but lack sufficient data to decompose the non-default probability term sub-structures. The implication is that bond prices are not dependent on future ratings, over and above non-default probability term structures (“survival rates”), as a mirror of default probability term structures, as the latter already contains all price-relevant information. At the same time, it may be unnecessary to decompose rating migration matrices, post default probability term structures.