Current Basel minimum capital requirements for credit risk under the Advanced Internal Rating Based Method (AIRB) use both probability of default (PD)and loss given default (LGD) as input parameters into a supervisory formula (Supervisory Formula). However, the Supervisory Formula stresses the PD and LGD parameters differently, and this disconnection undermines the theoretical consistency of the AIRB framework and leaves room for potential manipulation. This paper proposes a closed-form solution that mathematically ties the stressing of LGD and PD together, and therefore expands the current AIRB framework and establishes a simple methodology to estimate and stress test LGD.
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