Convexity and correlation effects in expected credit loss calculations for IFRS9/CECL and stress testing

This paper demonstrates that the convexity of PD functions as well as the correlation among probability of default (PD), loss given default (LGD) and exposure at default (EAD) outcomes impart skewness to the credit-loss, probability-distribution function (PDF) and thereby increase the expected values of credit losses (ECLs) by as much as 20 per cent or more according to estimates presented later. With regard to convexity, the magnitude of the effect on ECLs depends on the amount of convexity in PD functions as well as the extent of the random dispersion in the credit-risk factors that affect PDs. With regard to correlation, the magnitude of the effect depends on the amount of correlated variation in PD, LGD and EAD outcomes. In accounting for these effects, one may apply credit-cycle indices in modifying the existing PD, LGD and EAD models so that they produce point-in-time (PIT) estimates that move together over time in the way implied by common, credit-cycle effects. Having done that, an institution can account for convexity and correlation effects in producing the unbiased estimates of ECLs needed in determining losses under stress scenarios or impairments under IFRS9/CECL.