Full paper available here.
This paper develops a simple but rigorous approach to allowing for default probability risk in securitisation capital calculations. The approach consists of including additional random factors to describe risk in inputs, specifically default probabilities for pool loans. We show that the addition of such “parameter risk” translates into more conservative correlation assumptions for the asset correlations of the underlying loans.
Parameter risk is, hence, relevant for banks’ on-balance-sheet loans just as much as for securitisations secured on those loans. To the extent that parameter risk is correlated with systematic risk driving the bank’s wider portfolio, capital for loans should be increased. Securitisation capital, which depends on pool capital, should, in turn, be higher as well.
Parameter risk does not justify boosting securitisation capital for all the tranches in a deal beyond the level implied by prudent calculation of pool capital. It, therefore, does not provide an argument for deviations from capital neutrality under which the capital for all the tranches in a securitisation should equal that for the securitisation loan pool. (Reasons for non-neutrality includes the presence of agency costs created in complex, multi-agent securitisation processes.)
We believe that the Basel Committee allowed for parameter input risk in its original calibration of the Basel II capital risk weights for on-balance-sheet loans. Those involved in the calibration of Basel II were clearly aware that the correlation parameters employed in the Basel II risk weight functions were higher than those implied by statistical analysis of bank loan default data.
Our analysis shows that except where parameter risk implies higher pool capital, the impact on securitisation capital is relatively small. In particular, if parameter risk is correlated with intra-pool risk factors but is not systemic, then it justifies some limited shifting of capital towards more senior tranches. One might note that, if this latter type of parameter risk is present, the case for deduction of thin tranches attaching just below pool capital (a misguided and unjustified feature of current and proposed regulations) is even weaker.