This note describes an approach to calibrating the floor on capital used in the Basel rules for securitisation exposures held by banks. Under the Basel rules, the floor is currently set at value proportional to the par value of the securitisation position. No justification for the level specified has been provided by regulators nor for the use of a value equal to a percentage of par value.
Duponcheele et al (2024) argues that a risk sensitive approach should be followed in setting a capital floor, proposing a floor that is proportional to pool Risk Weights (RWs). Such an approach would seem natural since pool RWAs are the primary input to the capital formula. Pool RWs vary substantially across and, to some extent, within asset classes. Other things equal, this variability in risk is inherited by the tranched positions. So, allowing the floor to depend on the pool RWs appears justified.
How can one think about the calibration of a floor? One issue is the variability or uncertainty concerning the inputs to a capital calculation. One might focus on variability in the RWA input to the capital formula. However, banks in Europe are now required to allow for model risk in such risk parameters as Probabilities of Default and Loss Given Default (LGD) rates by adding conservative Margins of Conservatism (MoCs). Regulatory overrides based on uncertainty in PDs and LGDs appears to be double counting, therefore.
Capital formulae for tranched exposures depend on the correlation assumptions adopted for the underlying loans. The regulatory formula is based on the Simplified Supervisory Formula Approach (SSFA). This is an ad hoc formula rather than an explicit solution for marginal capital from a simplified Credit Portfolio Model (CPM) which is the case for the IRBA Risk Weight (RW) formula used for on-balance sheet loan exposures.
An explicit formula is, however, available in the form of the Pykhtin-Dev model (see Pykhtin and Dev (2002)), generalised in subsequent work to a multi-period version by Duponcheele, Perraudin and Totouom-Tangho l (2013). Within the Pykhtin-Dev model and its generalisation, the incremental correlation of individual loans within the pool is a key parameter (denoted ∗) that determines the spreading of on-balance-sheet pool capital across the different tranches of a securitisation. This note employs the model risk surrounding this ∗ as the basis for calibrating the capital floor.
