Credit risk management

1. Example Index
Copyright 2018 CapitaLogic Limited
Example Description Excel technique
1 EAD to one borrower
2 EAD to two borrowers
3 Independent homogeneous portfolio
4 Extreme case number of default
5 Normal random variable
6 Modelling default of one borrower with copula
7 Modelling default of two borrowers with copula
8 Modelling default of three borrower with copula
9 Vasicek default rate model
10 XCLs under the ECAI scale
11 Application of infinite homogeneous portfolio
12 Finite homogeneous portfolio Monte Carlo simulation
13 Percentile Percentile(…)
14 Numerical integration Numerical integration
15 Finite homogeneous portfolio Numerical integration
This Excel workbook is prepared in accordance with
Chapter 3 of the text book
"Managing Credit Risk Under The Basel III Framework, 3
rd
ed"
Authored by :Dr. LAM Yat-fai (林日辉)
Principal, Structured Products Analytics, CapitaLogic Limited
Adjunct Professor of Finance, City University of Hong Kong
Doctor of Business Administration
CFA, CAIA, CAMS, FRM, PRM
Website: https://sites.google.com/site/crmbase
E-mail: crmbasel@gmail.com
Copyright 2018 CapitaLogic Limited

2. Example 1 EAD to 1 borrower
Loan EAD LGD PD RM
1 10,000 90% 3% 1
Loan 1 Prob Default loss 1-year EL
Survive 97% 0 0
Default 3% 10,000 270
Portfolio 270
Copyright 2018 CapitaLogic Limited

3. Example 2 EAD to 2 borrowers
Loan EAD LGD PD RM
1 5,000 90% 3% 1
2 5,000 90% 3% 1
Loan 1 Loan 2 Prob Default loss 1-year EL
Survive Survive 94.09% 0 0
Survive Default 2.91% 5,000 131
Default Survive 2.91% 5,000 131
Default Default 0.09% 10,000 8
Portfolio 270
Copyright 2018 CapitaLogic Limited

4. Example 3 Independent homogeneous
k NOBCk PD
k
(1-PD)
NOB-k
Probability Confidence level Portfolio EAD 1,000,000
0 1 1 0.04755251 4.7553% 4.7553% LGD 90%
1 100 0.03 0.0490232 14.7070% 19.4622% PD 3%
2 4950 0.0009 0.05053939 22.5153% 41.9775%
3 161700 0.000027 0.05210246 22.7474% 64.7249% Extreme case no. of defaults 9
4 3921225 0.00000081 0.05371388 17.0606% 81.7855% XCDR 9.00%
5 75287520 2.43E-08 0.05537513 10.1308% 91.9163% XCL 81,000
6 1192052400 7.29E-10 0.05708776 4.9610% 96.8772%
7 1.6008E+10 2.187E-11 0.05885336 2.0604% 98.9376%
8 1.8609E+11 6.561E-13 0.06067357 0.7408% 99.6784%
9 1.9022E+12 1.9683E-14 0.06255007 0.2342% 99.9126%
10 1.731E+13 5.9049E-16 0.06448461 0.0659% 99.9785%
11 1.4163E+14 1.7715E-17 0.06647898 0.0167% 99.9952%
12 1.0504E+15 5.3144E-19 0.06853503 0.0038% 99.9990%
13 7.1105E+15 1.5943E-20 0.07065467 0.0008% 99.9998%
14 4.4187E+16 4.783E-22 0.07283987 0.0002% 100.0000%
15 2.5334E+17 1.4349E-23 0.07509265 0.0000% 100.0000%
16 1.3459E+18 4.3047E-25 0.0774151 0.0000% 100.0000%
17 6.6501E+18 1.2914E-26 0.07980938 0.0000% 100.0000%
18 3.0665E+19 3.8742E-28 0.08227771 0.0000% 100.0000%
19 1.3234E+20 1.1623E-29 0.08482238 0.0000% 100.0000%
20 5.3598E+20 3.4868E-31 0.08744576 0.0000% 100.0000%
21 2.0418E+21 1.046E-32 0.09015026 0.0000% 100.0000%
22 7.3321E+21 3.1381E-34 0.09293842 0.0000% 100.0000%
23 2.4865E+22 9.4143E-36 0.0958128 0.0000% 100.0000%
24 7.9776E+22 2.8243E-37 0.09877608 0.0000% 100.0000%
25 2.4252E+23 8.4729E-39 0.10183101 0.0000% 100.0000%
26 6.9957E+23 2.5419E-40 0.10498043 0.0000% 100.0000%
27 1.9174E+24 7.6256E-42 0.10822724 0.0000% 100.0000%
28 4.9988E+24 2.2877E-43 0.11157448 0.0000% 100.0000%
29 1.2411E+25 6.863E-45 0.11502524 0.0000% 100.0000%
30 2.9372E+25 2.0589E-46 0.11858272 0.0000% 100.0000%
Copyright 2018 CapitaLogic Limited

5. Example 4 Extreme case no. defaults
Portfolio EAD 1,000,000
LGD 90%
PD 3%
NOB 100
Extreme case no. of defaults 9
XCDR 9.00%
XCL 81,000
Copyright 2018 CapitaLogic Limited

6. Example 5 Normal random variable
Normal Cumulative Status
-0.3820545 0.35121047 0 PD 3%
-0.3097042 0.37839296 0 No. of ONEs 26
-1.2713012 0.10181075 0 % of ONEs 2.60%
-0.2494179 0.40151877 0
-1.4737046 0.07028057 0
1.97406242 0.97581268 0
-0.1379223 0.4451509 0
-0.3260081 0.37220912 0
-0.2023974 0.41980304 0
-0.1313501 0.44774918 0
-1.3232018 0.09288414 0
-0.500825 0.30824714 0
-0.3195038 0.37467224 0
-1.5794684 0.05711433 0
0.50325488 0.69260746 0
-0.3832153 0.35078008 0
1.33883956 0.90968855 0
-1.7586842 0.03931558 0
-1.1121688 0.13303278 0
1.29161216 0.90175426 0
0.49947074 0.6912761 0
-0.6856469 0.24646789 0
0.83975899 0.79947823 0
-1.3614016 0.0866934 0
-0.9985433 0.159008 0
-1.6049177 0.05425596 0
-0.0263867 0.48947447 0
-0.673935 0.25017633 0
0.01906484 0.50760531 0
-1.4120867 0.07896222 0
Copyright 2018 CapitaLogic Limited

7. Example 6 Copula for 1 borrower
Systematic Specific Normal Cumulative Status
-0.8695165 -0.2528026 -0.6149732 0.26928622 0 CCC 0.2
1.34074561 0.41207967 0.96817493 0.83352149 0 PD 3%
-1.3751438 0.85291451 0.14788691 0.55878399 0 No. of ONEs 39
-0.497075 0.69075884 0.39553478 0.65377587 0 % of ONEs 3.90%
-0.2231407 -0.1561212 -0.2394306 0.40538584 0
-0.2639281 0.0415136 -0.0809014 0.4677602 0
-1.0483274 -0.029501 -0.4952128 0.31022497 0
-0.7401109 -0.1367332 -0.4532855 0.32517158 0
0.07847377 0.08318118 0.10949405 0.54359468 0
-0.7561197 2.0852287 1.52693825 0.93661182 0
0.56233241 -0.3270881 -0.0410738 0.48361854 0
-0.6199954 -0.7734271 -0.9690447 0.16626145 0
-1.5031125 -1.4062557 -1.9300057 0.02680307 1
-0.9541383 -0.9640876 -1.2890097 0.09869735 0
-1.3643695 0.12109613 -0.5018529 0.30788549 0
0.68197611 1.17584898 1.35670029 0.91256177 0
0.32236265 0.26168945 0.37822712 0.64736906 0
-1.1214733 0.95974956 0.35688798 0.63941217 0
-0.690228 -0.4885018 -0.7456087 0.22795192 0
-0.6824609 1.32914722 0.88361961 0.81154921 0
-1.7743592 0.7005619 -0.166916 0.43371809 0
-0.3656699 -2.1973361 -2.1288897 0.01663169 1
-0.6965434 -3.2672689 -3.2338378 0.00061069 1
-1.6905286 -1.6998569 -2.2764256 0.01141028 1
2.67797943 -0.2112326 1.00869664 0.84343993 0
1.22476859 0.89177992 1.34536537 0.91074636 0
-0.6863315 0.35636725 0.01180777 0.50471051 0
-0.7298422 1.59191508 1.09745677 0.86377912 0
2.8772863 0.59982846 1.82326444 0.96586833 0
-0.0346368 -0.2734255 -0.2600493 0.39741288 0
Copyright 2018 CapitaLogic Limited

8. Example 7 Copula for 2 borrowers
Systematic Specific Normal Cumulative Status Specific Normal Cumulative Status
-1.4127516 -1.1827333 -1.6896706 0.0455455 0 1.50957419 0.71840246 0.76374542 0
1.49826357 0.15184074 0.80585432 0.78983657 0 -1.0250527 -0.2467911 0.40253493 0
1.03210209 0.21851406 0.657015 0.74441436 0 -1.2548204 -0.6607754 0.25437819 0
0.37472546 -1.245211 -0.9461682 0.1720314 0 -0.5476947 -0.3222908 0.37361622 0
1.1707275 -0.3861496 0.17818254 0.57071019 0 -1.0810842 -0.4433859 0.32874333 0
-0.1944975 1.62174664 1.36355236 0.91364575 0 0.15153903 0.0485587 0.51936451 0
1.36624505 -2.5148536 -1.6383501 0.05067434 0 -0.5693237 0.10178473 0.54053623 0
-1.0375476 -0.9585521 -1.3213605 0.0931906 0 -1.2744099 -1.6038723 0.05437111 0
0.65343695 1.71042786 1.82207907 0.96577851 0 1.26305746 1.42193883 0.92247799 0
-0.4834611 -2.0410424 -2.0417742 0.02058697 1 0.33984324 0.08775467 0.53496416 0
0.20474234 -1.3093189 -1.0795268 0.14017647 0 0.94011648 0.9324293 0.82444265 0
1.12832521 -0.1179313 0.3991214 0.65509812 0 -2.2512727 -1.5089971 0.06564976 0
-0.0256495 0.01308428 0.00023215 0.50009261 0 0.34981553 0.30141374 0.61845049 0
-0.1924776 -1.3642622 -1.3063119 0.09572326 0 0.17852201 0.07359633 0.5293342 0
-0.0189812 1.26775973 1.12543012 0.86979659 0 2.26057186 2.01342829 0.9779652 0
0.66148258 -0.3111891 0.01748803 0.50697636 0 1.10395221 1.28322888 0.90029405 0
-0.0485178 -1.0013833 -0.9173623 0.17947642 0 -0.3572822 -0.3412607 0.36645365 0
0.84491927 -0.0680928 0.31695529 0.62436124 0 -0.6078729 -0.1658387 0.43414194 0
-1.221511 0.14167729 -0.4195563 0.33740481 0 -0.2251016 -0.7476133 0.22734671 0
-1.2159815 -0.0060073 -0.5491765 0.29144216 0 0.07525415 -0.4764941 0.31686121 0
0.97397435 -0.1730682 0.28077765 0.61055953 0 -0.4527352 0.03063588 0.51222004 0
-1.7623417 1.21196528 0.29587155 0.61633591 0 -0.884502 -1.5792658 0.05713755 0
1.96716132 -0.9233469 0.05387473 0.52148251 0 -0.8768379 0.09547362 0.53803068 0
1.72294012 0.45101262 1.17392019 0.8797865 0 1.30699136 1.93953085 0.97378163 0
0.19403015 0.59941761 0.62290833 0.73332762 0 0.16884615 0.23779351 0.59397937 0
-0.783841 1.00875782 0.55171607 0.70942855 0 0.75579206 0.32545662 0.62758225 0
0.5785072 -0.0472217 0.2164799 0.58569315 0 0.09994416 0.34810906 0.63612086 0
0.20133629 2.50918777 2.3343261 0.99021067 0 1.59972294 1.52087602 0.93585452 0
1.68617983 0.1393989 0.87876471 0.81023557 0 -0.6508091 0.17198122 0.56827385 0
-3.0829927 -0.353605 -1.6950301 0.04503485 0 -1.0743247 -2.3396614 0.00965061 1
Copyright 2018 CapitaLogic Limited

9. Example 8 Copula for 3 borrowers
Systematic Specific Normal Cumulative Status Specific Normal Cumulative Status Specific Normal Cumulative Status
0.98932612 -1.8440454 -1.2069243 0.11373065 0 0.53932708 0.92482889 0.82247254 0 -0.0930433 0.35921963 0.6402846 0
0.06345279 -0.5465804 -0.4604994 0.32257889 0 -1.7973691 -1.5792388 0.05714064 0 -1.6585737 -1.4550965 0.07282128 0
0.36930451 0.36364923 0.49041576 0.68808014 0 -0.6187968 -0.3883107 0.34889306 0 -2.8969172 -2.4259235 0.00763474 1
0.0382591 0.45281918 0.42212378 0.66353266 0 2.05182804 1.85232078 0.96801011 0 -0.3523292 -0.2980228 0.38284288 0
0.78584837 0.58995304 0.87911212 0.81032976 0 1.60564355 1.78757332 0.96307756 0 1.0771307 1.31485706 0.90572103 0
-0.3832219 -0.2747258 -0.4171042 0.33830109 0 -0.159764 -0.3142793 0.37665447 0 0.48896348 0.26596019 0.60486507 0
-1.0888121 0.5059114 -0.0344307 0.48626687 0 1.00673632 0.41352076 0.66038744 0 -0.7909547 -1.194383 0.11616409 0
-0.4463411 -1.9937028 -1.9828318 0.02369311 1 -0.7900412 -0.9062441 0.18240333 0 1.37567062 1.0308274 0.84868912 0
-1.9725029 -0.3068749 -1.1566073 0.12371641 0 -1.259252 -2.0084393 0.02229831 1 0.94904042 -0.0332826 0.48672463 0
0.91637017 -0.4515556 0.0059296 0.50236555 0 2.17091462 2.35153826 0.99065202 0 -0.1413262 0.28340721 0.61156765 0
0.60988699 1.99756559 2.05942673 0.98027331 0 -1.4142916 -0.9922311 0.16054239 0 -0.1414487 0.14623417 0.55813173 0
-0.5227997 0.95392907 0.61941695 0.73217914 0 -0.1336081 -0.3533059 0.36192958 0 -0.9183907 -1.0552367 0.14565854 0
-0.6108308 -2.8618258 -2.8328667 0.00230663 1 -2.2778672 -2.3105583 0.01042863 1 0.3777863 0.06473048 0.5258057 0
-0.4365621 -1.4395332 -1.4827941 0.06906456 0 -0.4322761 -0.581876 0.28032509 0 0.16794708 -0.0450201 0.48204566 0
1.46231555 -0.8922973 -0.1441276 0.44269986 0 0.45370307 1.05977175 0.85537577 0 -0.5126645 0.19542635 0.57747041 0
-0.7411101 -0.3574465 -0.6511444 0.25747663 0 0.02649861 -0.3077334 0.37914259 0 0.32521034 -0.0405575 0.48382432 0
1.18541395 -0.9537975 -0.3229692 0.37335928 0 0.3484781 0.84182152 0.80005607 0 0.69019572 1.14746305 0.87440485 0
0.34085699 -0.765442 -0.5321963 0.29729503 0 -0.5640916 -0.352103 0.36238052 0 -0.2708547 -0.0898239 0.46421358 0
-0.6215469 0.4507091 0.12516226 0.54980245 0 0.58909999 0.24894284 0.5982975 0 -0.8395786 -1.0289061 0.1517619 0
1.86661645 -0.6486757 0.25458303 0.60047742 0 0.56322179 1.33853714 0.9096393 0 -1.0715981 -0.1236902 0.45078029 0
0.99803804 1.90788269 2.15279834 0.98433273 0 1.13302572 1.45974519 0.92781994 0 -1.8624934 -1.2195286 0.11132181 0
0.05057397 -0.7930122 -0.6866743 0.246144 0 -0.3729251 -0.310937 0.37792426 0 -1.8940993 -1.6715165 0.04730985 0
0.25570033 -0.0232489 0.0935582 0.53726994 0 0.58441729 0.63707138 0.73796082 0 0.48432873 0.54754945 0.70799935 0
0.97321738 -0.9103772 -0.3790301 0.35233275 0 -1.8047613 -1.1789915 0.11920077 0 0.14968596 0.56911923 0.71536239 0
0.32402827 -0.1218128 0.03595717 0.51434174 0 -0.1734752 -0.0102511 0.49591047 0 0.15529811 0.2838127 0.61172304 0
-0.8678838 -1.6585712 -1.8716006 0.03063094 0 -0.5208014 -0.8539484 0.1965668 0 0.26438006 -0.1516607 0.43972727 0
-0.2001606 0.05294451 -0.0421595 0.48318577 0 3.13296544 2.71269495 0.99666307 0 0.21717856 0.10473588 0.54170731 0
-1.4281888 0.97874784 0.23671323 0.59356036 0 1.29461207 0.51923078 0.69820009 0 -0.2150485 -0.8310507 0.20297249 0
-0.0728048 -1.3149941 -1.2087257 0.11338412 0 0.38168594 0.308831 0.62127496 0 -0.5785632 -0.5500419 0.2911453 0
1.87044511 0.37544594 1.17229754 0.87946119 0 0.90492912 1.64588169 0.95010594 0 0.11170066 0.93639659 0.82546548 0
Copyright 2018 CapitaLogic Limited

10. Example 9 Vasicerk default rate model
Mortgage QRRE Other retail Institution SME corp Large FI
Portfolio EAD 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000
LGD 90% 90% 90% 90% 90% 90%
PD 3% 3% 3% 3% 3% 3%
CCC 0.15 0.04 0.075491907 0.146775619 0.111220064 0.183469524
XCDR 0.229089152 0.098736263 0.141629975 0.225289958 0.183570802 0.26875979
XCL 206,180 88,863 127,467 202,761 165,214 241,884
Copyright 2018 CapitaLogic Limited

11. Example 10 XCLs under the ECAI scale
AA A BBB BB B
Portfolio EAD 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000
LGD 90% 90% 90% 90% 90%
PD 0.0333% 0.0834% 0.3345% 2.5652% 7.1682%
Exposure Mortgage QRRE Other retail Corporate Large FI
CCC 0.15 0.04 0.145639399 0.153277143 0.154164198
XCDR 0.008361479 0.00497199 0.048646791 0.210932402 0.392861772
XCL 7,525 4,475 43,782 189,839 353,576
Copyright 2018 CapitaLogic Limited

12. Example 11 Application of IHP
EAD LGD Rating RM EAD LGD PD RM
1 9696 51.51% A 1.57 Average 10,007.46 0.4998182 0.0834%
2 10477 50.84% A 1.51 SD 284.99964 0.0141534
3 9527 48.46% A 3.05 CV 2.85% 2.83%
4 9859 48.75% A 1.38
5 10272 51.71% A 1.10 Count 500 500 500
6 9637 48.78% A 2.83 Minimum 9501 0.4752 0.86
7 9572 49.92% A 3.06 Maximum 10494 0.525 3.06
8 9856 51.33% A 1.97 Below 1 year 2.80%
9 10350 49.76% A 1.47
10 10024 48.66% A 1.31
11 10395 51.20% A 1.82
12 10062 49.96% A 2.17 Portfolio EAD 5,003,730
13 9888 52.05% A 2.32 LGD 0.4998182
14 10337 50.37% A 1.72 PD 0.0834%
15 10414 49.66% A 1.00
16 10199 51.20% A 2.35 CCC 0.2350987
17 9920 51.31% A 1.85 XCDR 0.0299643
18 10454 49.16% A 2.23 XCL 74,939
19 10161 50.49% A 1.17
20 10308 52.14% A 1.83
21 9984 48.04% A 1.56
22 9944 51.97% A 2.95
23 10288 47.91% A 1.19
24 10040 48.74% A 2.75
25 10292 52.30% A 2.76
26 10168 51.40% A 1.78
27 9626 47.57% A 2.66
28 10250 50.02% A 1.73
29 10443 51.35% A 2.84
30 10424 51.47% A 2.51
31 9898 50.70% A 1.30
32 9557 52.45% A 2.95
Copyright 2018 CapitaLogic Limited

13. Example 12 Finite homogeneous
Borrower Specific Normal[0,1]Uniform[0,1] Default
1 0.448276 0.431367 0.666899 0 Systematic 0.001253
2 -0.03656 -0.03481 0.486118 0 No. of defaults 6
3 0.529765 0.509721 0.694876 0
4 -1.07633 -1.03456 0.150437 0 Extreme case no. of defaults 22
5 0.049079 0.047534 0.518956 0
6 0.943767 0.907789 0.818005 0
7 1.406924 1.353121 0.911991 0
8 -0.66825 -0.64219 0.260376 0
9 -0.06687 -0.06395 0.474504 0 Portfolio EAD 1,000,000
10 -0.84439 -0.81154 0.208527 0 LGD 90%
11 0.949221 0.913033 0.819387 0 PD 3%
12 0.22865 0.220195 0.58714 0 NOB 100
13 -1.31507 -1.26411 0.103095 0
14 1.53717 1.478354 0.930343 0 CCC 0.0755
15 -1.34574 -1.29361 0.097901 0 XCDR 22.00%
16 0.679961 0.654136 0.743488 0 XCL 198,000
17 -1.31561 -1.26463 0.103002 0
18 1.18176 1.136622 0.872152 0
19 1.183254 1.138059 0.872452 0
20 -2.31525 -2.2258 0.013014 1
21 0.94999 0.913772 0.819582 0
22 -0.85751 -0.82417 0.204923 0
23 0.813335 0.782377 0.783003 0
24 1.301197 1.251463 0.894617 0
25 -0.54789 -0.52646 0.299283 0
26 -0.0689 -0.06591 0.473725 0
27 -0.26515 -0.2546 0.399516 0
28 1.083709 1.042345 0.851374 0
29 -0.89527 -0.86047 0.194764 0
30 -0.56449 -0.54242 0.293764 0
Using
Monte Carlo simulation
Copyright 2018 CapitaLogic Limited

14. Example 13 Percentile
Order Number Sorted Percent Percentile
1 8246 3 10% 970.6
2 4491 15 50% 4941
3 3487 53 99.99% 9988.501
4 375 59
5 9645 65
6 653 75
7 9868 80
8 8135 81
9 2482 93
10 2070 94
11 2507 108
12 1385 113
13 4634 118
14 8423 128
15 8417 130
16 5274 141
17 8014 170
18 5751 171
19 8762 174
20 9229 176
21 922 178
22 7577 203
23 2729 206
24 7391 209
25 1434 211
26 176 213
27 3741 238
28 3 246
29 2213 246
30 5527 249
Copyright 2018 CapitaLogic Limited

15. Example 14 Numerical integration
Lower limit 1 2 3
Upper limit 2 3 4
x 1 2 3
f(x) 1 14.77811 0.366204
F(x) 3.75 32.78202 0.357432
Copyright 2018 CapitaLogic Limited

16. Example 15 Finite homogeneous
Portfolio EAD 1,000,000 Block Function Default Integrand
LGD 80% 1 3.77E-06 0 0.0000%
PD 3% 2 0.514627 1 0.0000%
NOB 100 3 0.485373 2 0.0000%
CCC 0.1468 3 0.0000%
4 0.0000%
No. of defaults 25 5 0.0000%
Default rate 25% 6 0.0000%
XCL 200,000 7 0.0000%
8 0.0000%
Lower limit -5 9 0.0000%
Upper limit 5 10 0.0000%
Variable -4.99766 11 0.0000%
Sum of integrands 2.78E-14 12 0.0000%
Integration 99.90% 13 0.0000%
14 0.0000%
15 0.0000%
16 0.0000%
17 0.0000%
18 0.0000%
19 0.0000%
20 0.0000%
21 0.0000%
22 0.0000%
23 0.0000%
24 0.0000%
25 0.0000%
26 0.0000%
27 0.0000%
28 0.0000%
29 0.0000%
30 0.0000%
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