Validation mythology of maturity adjustment formula for Basel II capital requirement

ABSTRACT In recent years considerable progress has been observed in the development of credit risk models. The Revised Framework on International Convergence of Capital Measurement and Capital Standards (2004) (Basel II) raised the standards of risk management to a new level. The validation methodologies of internal rating-based systems have emerged as an important issue for the implementation of Basel II. One of the less examined problems is the theoretical investigation of maturity effects and the probability of default time structure. The Basel Committee recommendations include maturity adjustment for capital requirements. However, the complete derivation of the proposed adjustment formula remains undisclosed. In this paper the authors describe a method of maturity adjustment calculation directly from open data published by rating agencies. In addition, analytical expressions revealing the probability of default time structure are proposed. In order to validate the Basel II recommendation a comparison of the results found with the Basel maturity adjustment formula is performed. The character of the presented dependences is close enough, but it was discovered that for low probabilities of default (for high ratings) and maturities of two to three years there may exist considerable underestimation of risk capital.