A proposed benchmark model using a modularised approach to calculate IFRS 9 expected credit loss

Figures & data

Table 1. Sample of accounts used

	MOB
	0	1	2	3	4
Account
A	0	1	0	0	0
B	0	0	3
C	0	0	0	1	1
D	0	0	0	2	2
E	0	0	0	0
F	0	0	0	1
G	0	2

Note that a zero represents accounts that are open and not in default, 1 represents accounts that went into default, 2 represents accounts that were closed, and a 3 represents accounts that are in default and were immediately closed.

Table 2. Calculated frequencies from sample data

	MOB
	0	1	2	3	4
Non-defaults $\left({\mathcal{F}}^N\right)$	7	6	5	3	2
Defaults $\left({\mathcal{F}}^D\right)$	0	1	1	2	1
Cured $\left({\mathcal{F}}^C\right)$	0	0	1	0	0
Closed Non-default $\left({\mathcal{F}}_C^N\right)$	0	1	0	1	1
Closed default $\left({\mathcal{F}}_C^D\right)$	0	0	1	0	0
Censored closed non-default $({\tilde{\mathcal{F}}}_C^N)$	0	0	1	0	0
Censored closed default $({\tilde{\mathcal{F}}}_C^D)$	0	0	0	1	0
Censored open non-default $({\tilde{\mathcal{F}}}_O^N)$	0	0	0	0	1
Censored open default $({\tilde{\mathcal{F}}}_O^D)$	0	0	0	0	1

Figure 1. Four monthly marginal probabilities for an unsecured loan portfolio

Figure 2. Term structure of the PD for an unsecured loan portfolio

Figure 3. Term structure of the PD based on different segmentations for an unsecured loan portfolio

Table 3. Representation of recovery data

Vintage($n$)	MOB ($t$)	EAD	Month since default ($i$)
			$0$	$1$	$\dots$	$I-1$	$I$
$1$	$1$	$EA{D}_{1,1}$	$AC{R}_{1,1,0}$	$AC{R}_{1,1,1}$	$\dots$	$AC{R}_{1,1,I-1}$	$AC{R}_{1,1,I}$
	$\dots$	$\dots$	$\dots$	$\dots$	$\dots$	$\dots$	$\dots$
	$T$	$EA{D}_{1,T}$	$AC{R}_{1,T,0}$	$AC{R}_{1,T,1}$	$\dots$	$AC{R}_{1,T,I-1}$	$AC{R}_{1,T,I}$
$2$	$1$	$EA{D}_{2,1}$	$AC{R}_{2,1,0}$	$AC{R}_{2,1,1}$	$\dots$	$AC{R}_{2,1,I-1}$
	$\dots$	$\dots$	$\dots$	$\dots$	$\dots$	$\dots$
	$T$	$EA{D}_{2,T}$	$AC{R}_{2,T,0}$	$AC{R}_{2,T,1}$	$\dots$	$AC{R}_{2,T,I-1}$
$\dots$	$\dots$	$\dots$	$\dots$	$\dots$
$N-1$	$1$	$EA{D}_{N-1,1}$	$AC{R}_{N-1,1,0}$	$AC{R}_{N-1,1,1}$
	$\dots$	$\dots$	$\dots$	$\dots$
	$T$	$EA{D}_{N-1,T}$	$AC{R}_{N-1,T,0}$	$AC{R}_{N-1,T,1}$
$N$	$1$	$EA{D}_{N,1}$	$AC{R}_{N,1,0}$
	$\dots$	$\dots$	$\dots$
	$T$	$EA{D}_{N,T}$	$AC{R}_{N,T,0}$

Figure 4. Actual LGD by month on book for the unsecured loan portfolio

Figure 5. Recovery rates per monthly vintage

Figure 6. LGD per month on book

Figure 7. Test sample accounts by contractual term of loan

Figure 8. Test sample accounts by month on book

Figure 9. Average PD term structure per month on book

Figure 10. Average PD term structure per month on book and per term

Figure 11. Distribution of PDs per stage and term

Figure 12. LGD comparison

Table 4. ECL comparison

	Case study	Benchmark	Exposure
	ECL	ECL
Stage 1	R 17 460	R 59 130	R 900 000
Stage 2	R 14 900	R 7 390	R 100 000
Total	R 32 360	R 66 520	R 1 000 000

Table 5. Exposure weighted 12-month PDs as percentage of bad rate

	Case study	Benchmark	Exposure
	12-Month PD	12-Month PD
Stage 1	39.14%	98.16%	R 900 000
Stage 2	236.70%	99.04%	R 100 000
Exposure weighted	58.93%	98.25%

Figure 13. PD term structure for different reference periods

Table 6. Summary of case study PD and benchmark PD

	Case study PD	Benchmark PD
PD term structure (Marginal PD)	Month since observation	Month on book
Default definition	Single default	Multiple default
Attrition	Modelled attrition as a separate component	Include in PD as closure rate

Figure 14. Benchmark PD term structure

Figure 15. Stage 1 ECL comparison

Figure 16. Stage 2 ECL comparison

Figure 17. Aggregate of Stage 1 and Stage 2 ECL comparison