Maturity adjustments under asymptotic single risk factor models: a comparative analysis

Eric McCoy

Abstract

ABSTRACT

Bank credit portfolios consist of instruments with different maturities. Both intuition and empirical evidence indicate that long-term credits are riskier than short-term credits. Consistent with these considerations, the Basel II maturity adjustment is a function of both maturity and default rate and is higher (in relative terms) for low default rate borrowers than for high default rate borrowers. This paper compares various methods to account for the maturity adjustment that fall within the framework of asymptotic single risk factor (ASRF) models. Section 2 reviews existing literature dealing with models of the maturity adjustment that fall within the scope of ASRF-type models. In particular, special attention is given to three approaches: (1) multi-period probability of default (PD) based on the theory of Merton (1974), (2) “annualized” PD using the theory of survival analysis and hazard rates and (3) default probability term structure derived from market credit spreads. Section 3 presents and analyzes the results obtained from simulating economic capital using both the Merton multi-period default approach and the “annualized” probability approach. As for the credit spread approach, instead of simulating portfolio economic capital, a case study on a single obligor is used to illustrate the concepts.