On meeting capital requirements with a chance-constrained optimization model

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Table 4 Possible migration paths of a 2 year BBB-rated loan

	Non-default m = 0	Migration m = 1	Paths m = 2		Default m = 0	Migration m = 1	Paths m = 2
1	BBB	AAA	AAA	1	BBB	D
2	BBB	AAA	AA	2	BBB	AAA	D
3	BBB	AAA	A	3	BBB	AA	D
4	BBB	AAA	BBB	4	BBB	A	D
5	BBB	AAA	BB	5	BBB	BBB	D
6	BBB	AAA	B	6	BBB	BB	D
7	BBB	AAA	C	7	BBB	B	D
8	BBB	AA	AAA	8	BBB	C	D
9	BBB	AA	AA
10	BBB	AA	A
11	BBB	AA	BBB
12	BBB	AA	BB
13	BBB	AA	B
14	BBB	AA	C
15	BBB	A	AAA
16	BBB	A	AA
17	BBB	A	A
18	BBB	A	BBB
19	BBB	A	BB
20	BBB	A	B
21	BBB	A	C
22	BBB	BBB	AAA
23	BBB	BBB	AA
24	BBB	BBB	A
25	BBB	BBB	BBB
26	BBB	BBB	BB
27	BBB	BBB	B
28	BBB	BBB	C
29	BBB	BB	AAA
30	BBB	BB	AA
31	BBB	BB	A
32	BBB	BB	BBB
33	BBB	BB	BB
34	BBB	BB	B
35	BBB	BB	C
36	BBB	B	AAA
37	BBB	B	AA
38	BBB	B	A
39	BBB	B	BBB
40	BBB	B	BB
41	BBB	B	B
42	BBB	B	C
43	BBB	C	AAA
44	BBB	C	AA
45	BBB	C	A
46	BBB	C	BBB
47	BBB	C	BB
48	BBB	C	B
49	BBB	C	C

	Non-default m = 0	Migration m = 1	Paths m = 2		Default m = 0	Migration m = 1	Paths m = 2
1	BBB	AAA	AAA	1	BBB	D
2	BBB	AAA	AA	2	BBB	AAA	D
3	BBB	AAA	A	3	BBB	AA	D
4	BBB	AAA	BBB	4	BBB	A	D
5	BBB	AAA	BB	5	BBB	BBB	D
6	BBB	AAA	B	6	BBB	BB	D
7	BBB	AAA	C	7	BBB	B	D
8	BBB	AA	AAA	8	BBB	C	D
9	BBB	AA	AA
10	BBB	AA	A
11	BBB	AA	BBB
12	BBB	AA	BB
13	BBB	AA	B
14	BBB	AA	C
15	BBB	A	AAA
16	BBB	A	AA
17	BBB	A	A
18	BBB	A	BBB
19	BBB	A	BB
20	BBB	A	B
21	BBB	A	C
22	BBB	BBB	AAA
23	BBB	BBB	AA
24	BBB	BBB	A
25	BBB	BBB	BBB
26	BBB	BBB	BB
27	BBB	BBB	B
28	BBB	BBB	C
29	BBB	BB	AAA
30	BBB	BB	AA
31	BBB	BB	A
32	BBB	BB	BBB
33	BBB	BB	BB
34	BBB	BB	B
35	BBB	BB	C
36	BBB	B	AAA
37	BBB	B	AA
38	BBB	B	A
39	BBB	B	BBB
40	BBB	B	BB
41	BBB	B	B
42	BBB	B	C
43	BBB	C	AAA
44	BBB	C	AA
45	BBB	C	A
46	BBB	C	BBB
47	BBB	C	BB
48	BBB	C	B
49	BBB	C	C

	Non-default m = 0	Migration m = 1	Paths m = 2		Default m = 0	Migration m = 1	Paths m = 2
1	BBB	AAA	AAA	1	BBB	D
2	BBB	AAA	AA	2	BBB	AAA	D
3	BBB	AAA	A	3	BBB	AA	D
4	BBB	AAA	BBB	4	BBB	A	D
5	BBB	AAA	BB	5	BBB	BBB	D
6	BBB	AAA	B	6	BBB	BB	D
7	BBB	AAA	C	7	BBB	B	D
8	BBB	AA	AAA	8	BBB	C	D
9	BBB	AA	AA
10	BBB	AA	A
11	BBB	AA	BBB
12	BBB	AA	BB
13	BBB	AA	B
14	BBB	AA	C
15	BBB	A	AAA
16	BBB	A	AA
17	BBB	A	A
18	BBB	A	BBB
19	BBB	A	BB
20	BBB	A	B
21	BBB	A	C
22	BBB	BBB	AAA
23	BBB	BBB	AA
24	BBB	BBB	A
25	BBB	BBB	BBB
26	BBB	BBB	BB
27	BBB	BBB	B
28	BBB	BBB	C
29	BBB	BB	AAA
30	BBB	BB	AA
31	BBB	BB	A
32	BBB	BB	BBB
33	BBB	BB	BB
34	BBB	BB	B
35	BBB	BB	C
36	BBB	B	AAA
37	BBB	B	AA
38	BBB	B	A
39	BBB	B	BBB
40	BBB	B	BB
41	BBB	B	B
42	BBB	B	C
43	BBB	C	AAA
44	BBB	C	AA
45	BBB	C	A
46	BBB	C	BBB
47	BBB	C	BB
48	BBB	C	B
49	BBB	C	C

	Non-default m = 0	Migration m = 1	Paths m = 2		Default m = 0	Migration m = 1	Paths m = 2
1	BBB	AAA	AAA	1	BBB	D
2	BBB	AAA	AA	2	BBB	AAA	D
3	BBB	AAA	A	3	BBB	AA	D
4	BBB	AAA	BBB	4	BBB	A	D
5	BBB	AAA	BB	5	BBB	BBB	D
6	BBB	AAA	B	6	BBB	BB	D
7	BBB	AAA	C	7	BBB	B	D
8	BBB	AA	AAA	8	BBB	C	D
9	BBB	AA	AA
10	BBB	AA	A
11	BBB	AA	BBB
12	BBB	AA	BB
13	BBB	AA	B
14	BBB	AA	C
15	BBB	A	AAA
16	BBB	A	AA
17	BBB	A	A
18	BBB	A	BBB
19	BBB	A	BB
20	BBB	A	B
21	BBB	A	C
22	BBB	BBB	AAA
23	BBB	BBB	AA
24	BBB	BBB	A
25	BBB	BBB	BBB
26	BBB	BBB	BB
27	BBB	BBB	B
28	BBB	BBB	C
29	BBB	BB	AAA
30	BBB	BB	AA
31	BBB	BB	A
32	BBB	BB	BBB
33	BBB	BB	BB
34	BBB	BB	B
35	BBB	BB	C
36	BBB	B	AAA
37	BBB	B	AA
38	BBB	B	A
39	BBB	B	BBB
40	BBB	B	BB
41	BBB	B	B
42	BBB	B	C
43	BBB	C	AAA
44	BBB	C	AA
45	BBB	C	A
46	BBB	C	BBB
47	BBB	C	BB
48	BBB	C	B
49	BBB	C	C