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Self-Consistency, Subjective Pricing, and a Theory of Credit Rating

We propose a theory for rating financial securities based on a concept of self-consistency, which does not allow issuers to gain, by tranching financial securities, from investors who rely on the rating criterion. While the expected loss criterion used by Moody's satisfies self-consistency, the probability of default criterion used by S&P does not. We find empirical evidences in the post-Dodd-Frank period (i.e., after July 2010) that the issuers may take advantage of the absence of self-consistency. We further propose a concept of scenario-relevance which reflects practical evaluation procedures of potential losses from defaultable securities. Our main theoretical results show that a self-consistent rating measure admits a Choquet integral representation, and this representation is also analytically tractable if one further takes economic scenarios into account. We suggest new examples of self-consistent and scenario-based rating criteria, such as ones based on the VaR and the Expected Shortfall.