119:; and as the network approaches complete integration the percentage of the first failures approaches zero. However, the integration increases the percentage of organizations that fail due to higher interconnection. In addition, up to some threshold, diversification does increase the percentage of discontinuous drops in value. Yet after the threshold level, the diversification decreases the percentage of failures: the authors say the following with respect to diversification: “it gets worse before it gets better”.
25:
111:
of the one organization are spread out among the other members of the network, given the fraction of the assets of the organization cross-held by other organizations is fixed. Integration refers to the fraction of the assets of the organization cross-held by other organizations given the number of
138:
Eliot, Golub and
Jackson (2013) provide an empirical method how to model cascades in financial networks. They assume that organizations in the network can cross hold assets of other organizations in the network. Also, they assume that players outside of the network can hold assets of the
92:. It can be defined as the discontinuous value loss (e.g. default) of the organization caused by the discontinuous value loss of another organization in the network. There are three conditions required for a cascade, there are; a failure, contagion and interconnection.
98:
and integration in the financial network determine whether and how failures will spread. Using the data on cross-holdings of organizations and on the value of organizations, it is possible to construct the dependency matrix to simulate cascades in the financial network.
757:
1125:
519:
1405:
382:
852:
1206:
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626:
268:
313:
566:
1438:
892:
414:
213:
966:
935:
182:
1238:
1458:
989:
419:
The authors find the equity value of an organization using the works by
Brioschi, Buzzachi and Colombo (1989) and Fedina, Hodder and Trianitis (1994):
637:
524:
The equity value is defined as the value of primitive assets and the value of claims on the primitive assets in other organizations in the network.
1008:
107:
Elliot, Golub and
Jackson (2013) characterize the financial network by diversification and integration. Diversification means to which extent
122:
Intuitively, the higher the threshold value for the discontinuous drop in the organization’s value the higher the percentage of failures is.
1555:
Brioschi, F., Buzzachi, Land
Colombo, M.M. 1989. "Risk Capital Financing and the Separation of Ownership and Control in Business Groups,"
125:
The authors conclude that the financial network is most susceptible to cascades if it has medium diversification and medium integration.
425:
88:
in another member of the financial network. In an extreme this can cause failure of the whole network in what is known as
941:
goes below this value, then a discontinuous drop in value happens and the organization fails. The cap on failure costs is
1299:
143:
Their model starts with the following assumptions (all notations are borrowed from Elliot, Golub and
Jackson (2013)):
64:
1603:
35:
1568:
Fedina, M., Hodder J.E. and
Trianitis A.J. 1994. "Cross Holdings Estimation Issues, Biases, and Distorntions,"
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779:
1136:
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1243:
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1510:
95:
577:
234:
42:
1588:
282:
533:
81:
1413:
910:
The equity value and the market value equations are extended by introducing threshold value
867:
389:
188:
944:
913:
160:
1214:
115:
Using random network, the authors show that high integration decreases the percentage of
8:
1443:
974:
1482:
85:
41:
The references used may be made clearer with a different or consistent style of
1477:
752:{\displaystyle v_{i}=\sum _{k}D_{ik}p_{k}+\sum _{j}C_{ij}-\sum _{j}C_{ji}V_{i}}
46:
1582:
1487:
527:
The counterpart of the equation above in terms of matrix algebra is given by
89:
1506:
Elliott, M., Golub, B. and
Jackson 2013. M Financial Networks and Contagion
1120:{\displaystyle V_{i}=\sum _{k}D_{ik}p_{k}+\sum _{j}C_{ij}V_{j}-k_{i}I_{i}}
1544:
1528:
1507:
1511:
http://www.its.caltech.edu/~melliott/papers/financial_networks.pdf
514:{\displaystyle V_{i}=\sum _{k}D_{ik}p_{k}+\sum _{j}C_{ij}V_{j}}
108:
1130:
Using matrix algebra, the expression above is equivalent to
991:
be an indicator function that is equal to 1 if the value of
770:
less the claims of other organizations in the network on i.
150:
There are m "primitive" assets (e.g. factors of production)
1293:
The market value including failure costs is given then by
270:
is a fraction of primitive assets of the organization
16:
Failure of one institution triggering further failures
1446:
1416:
1302:
1246:
1217:
1139:
1011:
977:
947:
916:
870:
782:
640:
580:
536:
428:
392:
386:
F is a n by n matrix whose diagonal element is :
328:
285:
237:
191:
163:
139:organizations in the network. They call the letter
1452:
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1399:
1282:
1232:
1200:
1119:
983:
960:
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846:
751:
620:
560:
513:
408:
376:
320:is a n by n matrix with zeros as diagonal elements
307:
262:
207:
176:
102:
1400:{\displaystyle v=F(I-C)^{-1}(Dp-b(v))=A(Dp-b(v))}
1580:
995:is below the threshold and 0 if the value of
1440:represents the fraction of failure costs of
147:There are n organizations that form a set N=
1539:Elliott, M., Golub, B. and Jackson 2013. M
1524:Elliott, M., Golub, B. and Jackson 2013. M
80:are situations in which the failure of one
112:the organizations cross-holding is fixed.
65:Learn how and when to remove this message
377:{\displaystyle F_{ii}=1-\sum _{j}C_{ji}}
133:
1581:
847:{\displaystyle v=FV=F(I-C)^{-1}Dp=ADp}
1201:{\displaystyle V=(I-C)^{-1}(Dp-b(v))}
905:
1520:
1518:
18:
937:. If the value of the organization
13:
14:
1615:
1545:https://ssrn.com/abstract=2175056
1529:https://ssrn.com/abstract=2175056
1515:
1508:https://ssrn.com/abstract=2175056
1541:Financial Networks and Contagion
1526:Financial Networks and Contagion
1283:{\displaystyle b_{i}=k_{i}I_{i}}
23:
1570:The Review of Financial Studies
1557:Journal of Banking and Finance,
902:holds directly and indirectly.
631:The market value is defined by
103:Diversification and integration
1562:
1549:
1533:
1500:
1394:
1391:
1385:
1370:
1361:
1358:
1352:
1337:
1325:
1312:
1227:
1221:
1195:
1192:
1186:
1171:
1159:
1146:
1002:Then the equity value becomes
814:
801:
621:{\displaystyle V=(I-C)^{-1}Dp}
600:
587:
263:{\displaystyle C_{ij}\geq \ 0}
78:Cascades in financial networks
1:
1493:
7:
1471:
894:represents the fraction of
10:
1620:
1240:is a vector whose element
861:is the dependence matrix.
274:held by the organization
153:Market price of an asset
128:
999:is above the threshold.
308:{\displaystyle C_{ii}=0}
215:is a share of the asset
1604:Financial risk modeling
766:is the equity value of
561:{\displaystyle V=Dp+CV}
1454:
1434:
1433:{\displaystyle A_{ij}}
1401:
1284:
1234:
1202:
1121:
985:
962:
931:
898:primitive assets that
888:
887:{\displaystyle A_{ij}}
848:
753:
622:
562:
515:
410:
409:{\displaystyle F_{ii}}
378:
309:
264:
209:
208:{\displaystyle D_{ik}}
178:
1455:
1435:
1402:
1285:
1235:
1203:
1122:
986:
963:
961:{\displaystyle k_{i}}
932:
930:{\displaystyle t_{i}}
889:
849:
754:
623:
563:
516:
411:
379:
310:
265:
229:is then n by m matrix
219:that an organization
210:
179:
177:{\displaystyle p_{k}}
141:outside shareholders.
134:Without Failure Costs
82:financial institution
1444:
1414:
1300:
1244:
1233:{\displaystyle b(v)}
1215:
1137:
1009:
975:
945:
914:
868:
780:
638:
578:
534:
426:
390:
326:
283:
235:
189:
161:
773:The letter implies
571:The letter implies
1450:
1430:
1397:
1280:
1230:
1198:
1117:
1070:
1034:
981:
958:
927:
906:With Failure Costs
884:
844:
749:
725:
699:
663:
618:
558:
511:
487:
451:
406:
374:
360:
305:
260:
205:
174:
1599:Financial markets
1483:Interbank network
1453:{\displaystyle j}
1061:
1025:
984:{\displaystyle I}
716:
690:
654:
478:
442:
351:
256:
86:cascading failure
75:
74:
67:
1611:
1594:Financial crises
1573:
1566:
1560:
1553:
1547:
1537:
1531:
1522:
1513:
1504:
1459:
1457:
1456:
1451:
1439:
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1431:
1429:
1428:
1406:
1404:
1403:
1398:
1336:
1335:
1289:
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1278:
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1268:
1256:
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1239:
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1207:
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1204:
1199:
1170:
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1126:
1124:
1123:
1118:
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1115:
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1083:
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987:
982:
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936:
934:
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926:
925:
893:
891:
890:
885:
883:
882:
853:
851:
850:
845:
825:
824:
762:Market value of
758:
756:
755:
750:
748:
747:
738:
737:
724:
712:
711:
698:
686:
685:
676:
675:
662:
650:
649:
627:
625:
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619:
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567:
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559:
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517:
512:
510:
509:
500:
499:
486:
474:
473:
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463:
450:
438:
437:
415:
413:
412:
407:
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404:
383:
381:
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373:
372:
359:
341:
340:
314:
312:
311:
306:
298:
297:
269:
267:
266:
261:
254:
250:
249:
214:
212:
211:
206:
204:
203:
183:
181:
180:
175:
173:
172:
90:systemic failure
70:
63:
59:
56:
50:
27:
26:
19:
1619:
1618:
1614:
1613:
1612:
1610:
1609:
1608:
1579:
1578:
1577:
1576:
1567:
1563:
1554:
1550:
1538:
1534:
1523:
1516:
1505:
1501:
1496:
1474:
1445:
1442:
1441:
1421:
1417:
1415:
1412:
1411:
1328:
1324:
1301:
1298:
1297:
1274:
1270:
1264:
1260:
1251:
1247:
1245:
1242:
1241:
1216:
1213:
1212:
1162:
1158:
1138:
1135:
1134:
1111:
1107:
1101:
1097:
1088:
1084:
1075:
1071:
1065:
1052:
1048:
1039:
1035:
1029:
1016:
1012:
1010:
1007:
1006:
976:
973:
972:
952:
948:
946:
943:
942:
921:
917:
915:
912:
911:
908:
875:
871:
869:
866:
865:
817:
813:
781:
778:
777:
743:
739:
730:
726:
720:
704:
700:
694:
681:
677:
668:
664:
658:
645:
641:
639:
636:
635:
603:
599:
579:
576:
575:
535:
532:
531:
505:
501:
492:
488:
482:
469:
465:
456:
452:
446:
433:
429:
427:
424:
423:
397:
393:
391:
388:
387:
365:
361:
355:
333:
329:
327:
324:
323:
290:
286:
284:
281:
280:
242:
238:
236:
233:
232:
196:
192:
190:
187:
186:
168:
164:
162:
159:
158:
136:
131:
105:
96:Diversification
71:
60:
54:
51:
40:
34:has an unclear
28:
24:
17:
12:
11:
5:
1617:
1607:
1606:
1601:
1596:
1591:
1575:
1574:
1561:
1548:
1532:
1514:
1498:
1497:
1495:
1492:
1491:
1490:
1485:
1480:
1478:Financial risk
1473:
1470:
1449:
1427:
1424:
1420:
1408:
1407:
1396:
1393:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1369:
1366:
1363:
1360:
1357:
1354:
1351:
1348:
1345:
1342:
1339:
1334:
1331:
1327:
1323:
1320:
1317:
1314:
1311:
1308:
1305:
1277:
1273:
1267:
1263:
1259:
1254:
1250:
1229:
1226:
1223:
1220:
1209:
1208:
1197:
1194:
1191:
1188:
1185:
1182:
1179:
1176:
1173:
1168:
1165:
1161:
1157:
1154:
1151:
1148:
1145:
1142:
1128:
1127:
1114:
1110:
1104:
1100:
1096:
1091:
1087:
1081:
1078:
1074:
1068:
1064:
1060:
1055:
1051:
1045:
1042:
1038:
1032:
1028:
1024:
1019:
1015:
980:
955:
951:
924:
920:
907:
904:
881:
878:
874:
855:
854:
843:
840:
837:
834:
831:
828:
823:
820:
816:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
760:
759:
746:
742:
736:
733:
729:
723:
719:
715:
710:
707:
703:
697:
693:
689:
684:
680:
674:
671:
667:
661:
657:
653:
648:
644:
629:
628:
617:
614:
609:
606:
602:
598:
595:
592:
589:
586:
583:
569:
568:
557:
554:
551:
548:
545:
542:
539:
522:
521:
508:
504:
498:
495:
491:
485:
481:
477:
472:
468:
462:
459:
455:
449:
445:
441:
436:
432:
417:
416:
403:
400:
396:
384:
371:
368:
364:
358:
354:
350:
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321:
315:
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296:
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259:
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171:
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148:
135:
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127:
117:first failures
104:
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36:citation style
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3:
2:
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1592:
1590:
1589:Systemic risk
1587:
1586:
1584:
1571:
1565:
1558:
1552:
1546:
1542:
1536:
1530:
1527:
1521:
1519:
1512:
1509:
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1499:
1489:
1488:Systemic risk
1486:
1484:
1481:
1479:
1476:
1475:
1469:
1467:
1463:
1447:
1425:
1422:
1418:
1388:
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1379:
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1295:
1294:
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1183:
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1177:
1174:
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1155:
1152:
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1143:
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1133:
1132:
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1108:
1102:
1098:
1094:
1089:
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1079:
1076:
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1053:
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1043:
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1036:
1030:
1026:
1022:
1017:
1013:
1005:
1004:
1003:
1000:
998:
994:
978:
971:Further, let
969:
953:
949:
940:
922:
918:
903:
901:
897:
879:
876:
872:
862:
860:
841:
838:
835:
832:
829:
826:
821:
818:
810:
807:
804:
798:
795:
792:
789:
786:
783:
776:
775:
774:
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769:
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740:
734:
731:
727:
721:
717:
713:
708:
705:
701:
695:
691:
687:
682:
678:
672:
669:
665:
659:
655:
651:
646:
642:
634:
633:
632:
615:
612:
607:
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596:
593:
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584:
581:
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552:
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546:
543:
540:
537:
530:
529:
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506:
502:
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493:
489:
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479:
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470:
466:
460:
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434:
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421:
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398:
394:
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366:
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32:This article
30:
21:
20:
1569:
1564:
1556:
1551:
1540:
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1465:
1461:
1410:The element
1409:
1292:
1210:
1129:
1001:
996:
992:
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938:
909:
899:
895:
864:The element
863:
858:
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772:
767:
763:
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630:
570:
526:
523:
418:
317:
275:
271:
226:
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106:
94:
77:
76:
61:
52:
33:
1559:13, 742-772
55:August 2013
1583:Categories
1572:, 7, 61-69
1494:References
1464:incurs if
47:footnoting
1380:−
1347:−
1330:−
1319:−
1181:−
1164:−
1153:−
1095:−
1063:∑
1027:∑
819:−
808:−
718:∑
714:−
692:∑
656:∑
605:−
594:−
480:∑
444:∑
353:∑
349:−
252:≥
84:causes a
1472:See also
43:citation
1468:fails.
1211:where
857:where
255:
129:Models
109:assets
1543:p.20
1460:that
223:holds
45:and
896:j's
157:is
1585::
1517:^
1290:.
968:.
1466:j
1462:i
1448:j
1426:j
1423:i
1419:A
1395:)
1392:)
1389:v
1386:(
1383:b
1377:p
1374:D
1371:(
1368:A
1365:=
1362:)
1359:)
1356:v
1353:(
1350:b
1344:p
1341:D
1338:(
1333:1
1326:)
1322:C
1316:I
1313:(
1310:F
1307:=
1304:v
1276:i
1272:I
1266:i
1262:k
1258:=
1253:i
1249:b
1228:)
1225:v
1222:(
1219:b
1196:)
1193:)
1190:v
1187:(
1184:b
1178:p
1175:D
1172:(
1167:1
1160:)
1156:C
1150:I
1147:(
1144:=
1141:V
1113:i
1109:I
1103:i
1099:k
1090:j
1086:V
1080:j
1077:i
1073:C
1067:j
1059:+
1054:k
1050:p
1044:k
1041:i
1037:D
1031:k
1023:=
1018:i
1014:V
997:i
993:i
979:I
954:i
950:k
939:i
923:i
919:t
900:i
880:j
877:i
873:A
859:A
842:p
839:D
836:A
833:=
830:p
827:D
822:1
815:)
811:C
805:I
802:(
799:F
796:=
793:V
790:F
787:=
784:v
768:i
764:i
745:i
741:V
735:i
732:j
728:C
722:j
709:j
706:i
702:C
696:j
688:+
683:k
679:p
673:k
670:i
666:D
660:k
652:=
647:i
643:v
616:p
613:D
608:1
601:)
597:C
591:I
588:(
585:=
582:V
556:V
553:C
550:+
547:p
544:D
541:=
538:V
507:j
503:V
497:j
494:i
490:C
484:j
476:+
471:k
467:p
461:k
458:i
454:D
448:k
440:=
435:i
431:V
402:i
399:i
395:F
370:i
367:j
363:C
357:j
346:1
343:=
338:i
335:i
331:F
318:C
303:0
300:=
295:i
292:i
288:C
276:i
272:j
258:0
247:j
244:i
240:C
227:D
221:i
217:k
201:k
198:i
194:D
170:k
166:p
155:k
68:)
62:(
57:)
53:(
49:.
39:.
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