Decomposing Rating Migration Matrices from Market Prices Revisited

Abstract

The study revisits the method and premises of decomposing rating migration matrices from price data. Significantly easier, and more accurate method is presented. As an intermediary step, 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 the decomposed default probability term structures. 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. Furthermore, it is shown that this is not a matter of insufficient price data. Additional price data cannot solve this, and push the outcome to a global solution. The main implications are twofold: First, the underlying issue is that rating migration matrices state and reveal 2 components: a) default and non-default probability term structures, and b) non-default probability term sub-structures. The latter refers to a break-down of future non-default probabilities, per rating category – future rating probabilities in essence. Price data contain sufficient information to decompose the former, but not the latter. It is generally not possible to make non-default probability sub-structures (future rating probabilities) relevant in some way – to relate it to certain data – to allow decomposition, because there is little (market) data pertaining to this. 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. Secondly, rating migration matrices can be decomposed accurately enough, to provide some insight. At the same time, it may be unnecessary to decompose rating migration matrices, post default probability term structures. The latter can be done accurately and easily, and contain all the relevant price information.