1083:
are required to compute the value of CVA. Calculating CVA risk would require 250 daily market risk scenarios over the 12-month stress period. CVA has to be calculated for each market risk scenario, resulting in 250 million simulations. These calculations have to be repeated across 6 risk types and 5
62:
The "CVA charge". The hedging of the CVA desk has a cost associated to it, i.e. the bank has to buy the hedging instrument. This cost is then allocated to each business line of an investment bank (usually as a contra revenue). This allocated cost is called the "CVA
1061:
A good introduction can be found in a paper by
Michael Pykhtin and Steven Zhu. Karlsson et al. (2016) present a numerical efficient method for calculating expected exposure, potential future exposure and CVA for interest rate derivatives, in particular Bermudan
893:
757:
373:
1248:
590:
792:
800:
501:
427:
530:
1194:
477:
630:
610:
550:
451:
396:
907:
on all risk factors; this is computationally demanding. There exists a simple approximation for CVA. This consists in buying default protection, typically a
654:
1181:
183:
1079:'s July 2015 consultation document regarding CVA calculations, if CVA is calculated using 100 timesteps with 10,000 scenarios per timestep, 1 million
1128:
1331:
1282:
1224:
1301:
1076:
1252:
103:. "CVA" can refer more generally to several related concepts, as delineated aside. The most common transactions attracting CVA involve
161:
as well as on the market risk factors that drive derivatives' values and, therefore, exposure. It is typically calculated under
1286:
1080:
162:
1321:
1198:
1023:
on the net CVA-risk, the CVA desk is responsible also for managing (minimizing) the capital requirements under Basel.
108:
1316:
1220:
1037:
1012:
974:
956:
1159:
104:
92:
927:
a portion of profits on uncollateralized financial derivatives. These reserved profits can be viewed as the
95:
during the life of the transaction. CVA is one of a family of related valuation adjustments, collectively
904:
888:{\displaystyle \mathrm {EE} ^{*}(t)=\mathbb {E} \left\lbrack {{\frac {B_{0}}{B_{t}}}~E(t)}\right\rbrack }
555:
138:
80:
765:
1326:
1231:
1032:
1008:
924:
174:
158:
84:
996:
908:
633:
142:
112:
100:
33:
1020:
982:
962:
480:
399:
1142:
1124:
928:
920:
154:
911:, netted for each counterparty. The CDS price may then be used to back out the CVA charge.
486:
405:
1143:"Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method"
1104:
1004:
506:
1266:
1108:
456:
1000:
752:{\displaystyle \mathrm {CVA} =LGD\int _{0}^{T}\mathrm {EE} ^{*}(t)~d\mathrm {PD} (0,t)}
645:
615:
595:
535:
436:
381:
1310:
985:, increasingly CVA pricing and hedging is under the "ownership" of a centralized CVA
430:
141:
one defines CVA as the difference between the risk-free portfolio value and the true
177:
expectation of the discounted loss. The risk-neutral expectation can be written as
986:
978:
150:
146:
88:
44:
1163:
368:{\displaystyle \mathrm {CVA(T)} =E^{Q}=\int _{0}^{T}E^{Q}\leftd\mathrm {PD} (0,t)}
1249:"Simple Derivatives CVA Calculation Example (Credit valuation adjustment) excel"
932:
1063:
1016:
116:
53:
hedge to reduce the amount of capital required under the CVA calculation of
648:
greatly simplifies the analysis. Under this assumption this simplifies to
993:
936:
120:
54:
37:
1084:
liquidity horizons, resulting in potentially 8.75 billion simulations.
939:
changes in counterparty risk will result in earnings volatility; see
592:
is the risk neutral probability of counterparty default between times
992:
In particular, this desk addresses volatility in earnings due to the
977:). Whereas historically, this exposure was a concern of both the
1283:
Counterparty credit risk pricing, assessment, and dynamic hedging
632:. These probabilities can be obtained from the term structure of
1141:
Patrik
Karlsson, Shashi Jain. and Cornelis W. Oosterlee (2016).
1302:
Credit
Valuation Adjustment (CVA) - Corporate Finance Institute
1042:
952:
940:
132:
96:
1195:"The Triple Convergence Of Credit Valuation Adjustment (CVA)"
433:
invested today at the prevailing interest rate for maturity
270:
644:
Assuming independence between exposure and counterparty's
1007:
here focuses on addressing changes to the counterparty's
794:
is the risk-neutral discounted expected exposure (EE):
165:. (Which can become computationally intensive; see .)
50:
hedge for possible losses due to counterparty default;
18:
803:
768:
657:
618:
598:
558:
538:
509:
489:
459:
439:
408:
384:
186:
157:. This price adjustment will depend on counterparty
1118:
1116:
119:, and may also result in earnings volatility under
887:
786:
751:
624:
604:
584:
544:
524:
495:
471:
445:
421:
390:
367:
123:, and is therefore managed by a specialized desk.
935:embedded in the transaction. As outlined, under
961:In the course of trading and investing, Tier 1
903:The full calculation of CVA, as above, is via a
111:, and combinations thereof. CVA has a specific
1267:"The Long and Short of It: An Overview of XVA"
1125:"A Guide to Modeling Counterparty Credit Risk"
640:Exposure, independent of counterparty default
402:of the longest transaction in the portfolio,
145:that takes into account the possibility of a
101:Financial economics § Derivative pricing
8:
47:of an investment bank, whose purpose is to:
1015:at a given quantile. Further, since under
324:
318:
32:A part of the regulatory Capital and RWA (
29:The mathematical concept as defined below;
1265:Kenneth Kapner and Charles Gates (2016).
857:
847:
841:
840:
832:
831:
813:
805:
802:
778:
770:
767:
726:
705:
697:
690:
685:
658:
656:
617:
597:
559:
557:
537:
508:
488:
458:
438:
413:
407:
383:
342:
298:
288:
282:
258:
248:
243:
227:
214:
187:
185:
957:Financial risk management § Banking
149:'s default. In other words, CVA is the
1097:
1054:
429:is the future value of one unit of the
1077:Basel Committee on Banking Supervision
1019:, banks are required to hold specific
1109:Credit valuation adjustment framework
7:
999:requiring that CVA be considered in
91:to compensate it for taking on the
1123:Pykhtin, M.; Zhu, S. (July 2007).
809:
806:
774:
771:
730:
727:
701:
698:
665:
662:
659:
585:{\displaystyle \mathrm {PD} (s,t)}
563:
560:
346:
343:
200:
194:
191:
188:
14:
919:The CVA charge may be seen as an
787:{\displaystyle \mathrm {EE} ^{*}}
87:price, as charged by a bank to a
1251:. 7 October 2013. Archived from
1197:. Global Trading. Archived from
133:XVA § Valuation adjustments
99:; for further context here see
93:credit risk of that counterparty
36:) calculation introduced under
173:Unilateral CVA is given by the
1332:Monte Carlo methods in finance
877:
871:
825:
819:
746:
734:
717:
711:
579:
567:
519:
513:
362:
350:
315:
309:
233:
220:
203:
197:
1:
1193:Alvin Lee (17 August 2015).
1147:Applied Mathematical Finance
973:(expected positive/negative
953:XVA § Accounting impact
941:XVA § Accounting impact
109:foreign exchange derivatives
983:Middle Office finance teams
73:Credit valuation adjustment
1348:
1221:European Banking Authority
950:
130:
83:, is an "adjustment" to a
1180:CVA calculation example:
1164:"Valuation Adjustments 1"
1038:Potential future exposure
1013:potential future exposure
105:interest rate derivatives
1287:Citigroup Global Markets
947:Function of the CVA desk
532:is the exposure at time
503:is the time of default,
169:Risk-neutral expectation
155:counterparty credit risk
1182:Monte-Carlo with Python
965:generate counterparty
905:Monte-Carlo simulation
889:
788:
753:
626:
606:
586:
546:
526:
497:
473:
447:
423:
392:
369:
163:a simulation framework
22:CVA related concepts:
1230:. EBA. Archived from
951:Further information:
921:accounting adjustment
890:
789:
754:
627:
607:
587:
547:
527:
498:
496:{\displaystyle \tau }
474:
448:
424:
422:{\displaystyle B_{t}}
393:
370:
139:financial mathematics
131:Further information:
81:financial mathematics
1322:Mathematical finance
1223:(25 February 2015).
1201:on 11 September 2015
1033:Financial derivative
915:Accounting treatment
801:
766:
655:
616:
596:
556:
536:
525:{\displaystyle E(t)}
507:
487:
457:
437:
406:
382:
184:
1225:"EBA Report on CVA"
997:accounting standard
909:Credit Default Swap
695:
634:credit default swap
472:{\displaystyle LGD}
253:
34:risk-weighted asset
1281:James Lee (2010).
1021:regulatory capital
943:and next section.
885:
784:
749:
681:
622:
602:
582:
542:
522:
493:
481:loss given default
469:
443:
419:
388:
365:
239:
1317:Actuarial science
1075:According to the
1009:credit worthiness
981:trading desk and
929:net present value
867:
863:
722:
625:{\displaystyle t}
605:{\displaystyle s}
545:{\displaystyle t}
446:{\displaystyle t}
391:{\displaystyle T}
304:
69:
68:
1339:
1289:
1279:
1273:
1263:
1257:
1256:
1245:
1239:
1238:
1236:
1229:
1217:
1211:
1210:
1208:
1206:
1190:
1184:
1178:
1172:
1171:
1156:
1150:
1139:
1133:
1132:
1129:GARP Risk Review
1120:
1111:
1102:
1085:
1073:
1067:
1059:
1003:accounting. The
963:investment banks
894:
892:
891:
886:
884:
880:
865:
864:
862:
861:
852:
851:
842:
835:
818:
817:
812:
793:
791:
790:
785:
783:
782:
777:
758:
756:
755:
750:
733:
720:
710:
709:
704:
694:
689:
668:
631:
629:
628:
623:
611:
609:
608:
603:
591:
589:
588:
583:
566:
551:
549:
548:
543:
531:
529:
528:
523:
502:
500:
499:
494:
478:
476:
475:
470:
452:
450:
449:
444:
428:
426:
425:
420:
418:
417:
397:
395:
394:
389:
374:
372:
371:
366:
349:
338:
334:
323:
319:
305:
303:
302:
293:
292:
283:
263:
262:
252:
247:
232:
231:
219:
218:
206:
19:
1347:
1346:
1342:
1341:
1340:
1338:
1337:
1336:
1307:
1306:
1298:
1293:
1292:
1280:
1276:
1264:
1260:
1247:
1246:
1242:
1234:
1227:
1219:
1218:
1214:
1204:
1202:
1192:
1191:
1187:
1179:
1175:
1162:(May 3, 2016).
1158:
1157:
1153:
1140:
1136:
1122:
1121:
1114:
1105:Basel Committee
1103:
1099:
1094:
1089:
1088:
1074:
1070:
1060:
1056:
1051:
1029:
959:
949:
917:
901:
853:
843:
836:
804:
799:
798:
769:
764:
763:
696:
653:
652:
642:
636:(CDS) spreads.
614:
613:
594:
593:
554:
553:
534:
533:
505:
504:
485:
484:
455:
454:
435:
434:
409:
404:
403:
380:
379:
294:
284:
272:
269:
268:
264:
254:
223:
210:
182:
181:
171:
143:portfolio value
135:
129:
17:
12:
11:
5:
1345:
1343:
1335:
1334:
1329:
1324:
1319:
1309:
1308:
1305:
1304:
1297:
1296:External links
1294:
1291:
1290:
1274:
1258:
1255:on 2023-06-03.
1240:
1237:on 2015-06-07.
1212:
1185:
1173:
1151:
1134:
1112:
1096:
1095:
1093:
1090:
1087:
1086:
1068:
1053:
1052:
1050:
1047:
1046:
1045:
1040:
1035:
1028:
1025:
1001:mark-to-market
948:
945:
916:
913:
900:
897:
896:
895:
883:
879:
876:
873:
870:
860:
856:
850:
846:
839:
834:
830:
827:
824:
821:
816:
811:
808:
781:
776:
773:
760:
759:
748:
745:
742:
739:
736:
732:
729:
725:
719:
716:
713:
708:
703:
700:
693:
688:
684:
680:
677:
674:
671:
667:
664:
661:
646:credit quality
641:
638:
621:
601:
581:
578:
575:
572:
569:
565:
562:
541:
521:
518:
515:
512:
492:
468:
465:
462:
442:
416:
412:
398: is the
387:
376:
375:
364:
361:
358:
355:
352:
348:
345:
341:
337:
333:
330:
327:
322:
317:
314:
311:
308:
301:
297:
291:
287:
281:
278:
275:
271:
267:
261:
257:
251:
246:
242:
238:
235:
230:
226:
222:
217:
213:
209:
205:
202:
199:
196:
193:
190:
170:
167:
159:credit spreads
128:
125:
113:capital charge
67:
66:
65:
64:
60:
59:
58:
51:
41:
30:
24:
23:
16:Economics term
15:
13:
10:
9:
6:
4:
3:
2:
1344:
1333:
1330:
1328:
1325:
1323:
1320:
1318:
1315:
1314:
1312:
1303:
1300:
1299:
1295:
1288:
1284:
1278:
1275:
1272:
1268:
1262:
1259:
1254:
1250:
1244:
1241:
1233:
1226:
1222:
1216:
1213:
1200:
1196:
1189:
1186:
1183:
1177:
1174:
1169:
1165:
1161:
1155:
1152:
1148:
1144:
1138:
1135:
1130:
1126:
1119:
1117:
1113:
1110:
1106:
1101:
1098:
1091:
1082:
1078:
1072:
1069:
1065:
1058:
1055:
1048:
1044:
1041:
1039:
1036:
1034:
1031:
1030:
1026:
1024:
1022:
1018:
1014:
1011:, offsetting
1010:
1006:
1002:
998:
995:
990:
988:
984:
980:
976:
972:
968:
964:
958:
954:
946:
944:
942:
938:
934:
930:
926:
922:
914:
912:
910:
906:
899:Approximation
898:
881:
874:
868:
858:
854:
848:
844:
837:
828:
822:
814:
797:
796:
795:
779:
743:
740:
737:
723:
714:
706:
691:
686:
682:
678:
675:
672:
669:
651:
650:
649:
647:
639:
637:
635:
619:
599:
576:
573:
570:
539:
516:
510:
490:
482:
466:
463:
460:
440:
432:
431:base currency
414:
410:
401:
385:
359:
356:
353:
339:
335:
331:
328:
325:
320:
312:
306:
299:
295:
289:
285:
279:
276:
273:
265:
259:
255:
249:
244:
240:
236:
228:
224:
215:
211:
207:
180:
179:
178:
176:
168:
166:
164:
160:
156:
152:
148:
144:
140:
134:
126:
124:
122:
118:
114:
110:
106:
102:
98:
94:
90:
86:
82:
78:
74:
61:
56:
52:
49:
48:
46:
42:
39:
35:
31:
28:
27:
26:
25:
21:
20:
1277:
1270:
1261:
1253:the original
1243:
1232:the original
1215:
1203:. Retrieved
1199:the original
1188:
1176:
1167:
1154:
1146:
1137:
1100:
1071:
1057:
991:
979:Front Office
970:
966:
960:
918:
902:
761:
643:
377:
175:risk-neutral
172:
151:market value
147:counterparty
136:
89:counterparty
85:derivative's
76:
72:
70:
1327:Credit risk
1081:simulations
933:credit risk
127:Calculation
1311:Categories
1168:fincad.com
1092:References
1205:19 August
1160:John Hull
1064:swaptions
1017:Basel III
815:∗
780:∗
707:∗
683:∫
491:τ
332:τ
241:∫
229:∗
117:Basel III
1107:(2020).
1027:See also
975:exposure
923:made to
400:maturity
63:Charge".
43:The CVA
1005:hedging
994:IFRS 13
937:IFRS 13
931:of the
925:reserve
479:is the
121:IFRS 13
79:), in
55:Basel 3
38:Basel 3
955:, and
866:
762:where
721:
552:, and
378:where
115:under
1235:(PDF)
1228:(PDF)
1049:Notes
1271:GFMI
1207:2015
987:desk
969:and
612:and
45:desk
1043:XVA
971:ENE
967:EPE
153:of
137:In
97:xVA
77:CVA
1313::
1285:,
1269:.
1166:.
1149:.
1145:.
1127:.
1115:^
989:.
483:,
453:,
107:,
71:A
1209:.
1170:.
1131:.
1066:.
882:]
878:)
875:t
872:(
869:E
859:t
855:B
849:0
845:B
838:[
833:E
829:=
826:)
823:t
820:(
810:E
807:E
775:E
772:E
747:)
744:t
741:,
738:0
735:(
731:D
728:P
724:d
718:)
715:t
712:(
702:E
699:E
692:T
687:0
679:D
676:G
673:L
670:=
666:A
663:V
660:C
620:t
600:s
580:)
577:t
574:,
571:s
568:(
564:D
561:P
540:t
520:)
517:t
514:(
511:E
467:D
464:G
461:L
441:t
415:t
411:B
386:T
363:)
360:t
357:,
354:0
351:(
347:D
344:P
340:d
336:]
329:=
326:t
321:|
316:)
313:t
310:(
307:E
300:t
296:B
290:0
286:B
280:D
277:G
274:L
266:[
260:Q
256:E
250:T
245:0
237:=
234:]
225:L
221:[
216:Q
212:E
208:=
204:)
201:T
198:(
195:A
192:V
189:C
75:(
57:;
40:;
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.