Asymptotic Single Risk Factor Models with Stochastic and Correlated Loss Given Default

In line with the recent steer of the Basel Committee to foster a regulatory framework balancing greater risk-sensitivity, simplicity and comparability, we propose two extensions to the asymptotic single risk factor (ASRF) model in order to account for stochastic and correlated losses given default. In either setups, the strength of the PD-LGD link is controlled via a single additional risk parameter, as for the default dependence in the standard Basel framework. This parameter is connected to the correlation between the default rate and average observed loss given default, which is an observable statistic. We provide portfolio-invariant semi-analytical formulas for computing value-at-risk, solely by supplying new regulatory mapping functions translating unconditional LGDs into conditional LGDs. These ASRF extensions provide control on the PD-LGD link and give full flexibility regarding the choice of the marginal LGD distributions without disrupting the standard Basel machinery. This contributes to enhance regulatory capital computations by considering well-documented empirical evidence while maintaining computational tractability.