33:
640:
exposures in derivatives portfolios: first, a set of benchmark models is specified and calibrated to market prices of liquid instruments, then the target portfolio is priced under all benchmark models. A measure of exposure to model risk is then given by the difference between the current portfolio valuation and the worst-case valuation under the benchmark models. Such a measure may be used as a way of determining a reserve for model risk for derivatives portfolios.
580:
Model risk does not only exist for complex financial contracts. Frey (2000) presents a study of how market illiquidity is a source of model risk. He writes "Understanding the robustness of models used for hedging and risk-management purposes with respect to the assumption of perfectly liquid markets
626:
Another approach to model risk is the worst-case, or minmax approach, advocated in decision theory by Gilboa and
Schmeidler. In this approach one considers a range of models and minimizes the loss encountered in the worst-case scenario. This approach to model risk has been developed by Cont (2006).
520:
are most likely to suffer from model risk. He writes "I would think it's safe to say that there is no area where model risk is more of an issue than in the modeling of the volatility smile." Avellaneda & Paras (1995) proposed a systematic way of studying and mitigating model risk resulting from
630:
Jokhadze and
Schmidt (2018) propose several model risk measures using Bayesian methodology. They introduce superposed risk measures that incorporate model risk and enables consistent market and model risk management. Further, they provide axioms of model risk measures and define several practical
562:
Gennheimer investigates the model risk present in pricing basket default derivatives. He prices these derivatives with various copulas and concludes that "... unless one is very sure about the dependence structure governing the credit basket, any investors willing to trade basket default products
652:
Kato and
Yoshiba discuss qualitative and quantitative ways of controlling model risk. They write "From a quantitative perspective, in the case of pricing models, we can set up a reserve to allow for the difference in estimations using alternative models. In the case of risk measurement models,
639:
To measure the risk induced by a model, it has to be compared to an alternative model, or a set of alternative benchmark models. The problem is how to choose these benchmark models. In the context of derivative pricing Cont (2006) proposes a quantitative approach to measurement of model risk
761:, "translates into heightened dependence on these assumptions and, thus, higher model risk. As this risk should be expected to be priced by the market, part of the yield pick-up obtained relative to equally rated single obligor instruments is likely to be a direct reflection of model risk."
554:
Uncertainty on correlation parameters is another important source of model risk. Cont and
Deguest propose a method for computing model risk exposures in multi-asset equity derivatives and show that options which depend on the worst or best performances in a basket (so called
653:
scenario analysis can be undertaken for various fluctuation patterns of risk factors, or position limits can be established based on information obtained from scenario analysis." Cont (2006) advocates the use of model risk exposure for computing such reserves.
622:
Rantala (2006) mentions that "In the face of model risk, rather than to base decisions on a single selected 'best' model, the modeller can base his inference on an entire set of models by using model averaging." This approach avoids the "flaw of averages".
541:
is an input so that new observations on the yield curve can be used to update the model at regular frequencies. They explore the issue of time-consistent and self-financing strategies in this class of models. Model risk affects all the three main steps of
571:
Complexity of a model or a financial contract may be a source of model risk, leading to incorrect identification of its risk factors. This factor was cited as a major source of model risk for mortgage backed securities portfolios during the 2007 crisis.
648:
Jokhadze and
Schmidt (2018) introduce monetary market risk measures that covers model risk losses. Their methodology enables to harmonize market and model risk management and define limits and required capitals for risk positions.
449:
credit card transactions, and computing the probability of an air flight passenger being a terrorist. In fact, Burke regards failure to use a model (instead over-relying on expert judgment) as a type of model risk.
741:' is one such adaptation. But they find it preferable to fudge one parameter, namely volatility, and make it a function of time to expiry and strike price, rather than have to precisely estimate another."
516:
Volatility is the most important input in risk management models and pricing models. Uncertainty on volatility leads to model risk. Derman believes that products whose value depends on a
745:
However, Cherubini and Della Lunga describe the disadvantages of parsimony in the context of volatility and correlation modelling. Using an excessive number of parameters may induce
605:
technology, which can be particularly prone to implementation errors. Mitigation strategies include adding consistency checks, validating inputs, and using specialized tools. See
563:
should imperatively compute prices under alternative copula specifications and verify the estimation errors of their simulation to know at least the model risks they run".
593:
can often be illiquid and difficult to value. Hedge funds that trade these securities can be exposed to model risk when calculating monthly NAV for its investors.
1388:
865:
1057:
Buraschi, A.; Corielli, F. (2005). "Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models".
749:
while choosing a severely specified model may easily induce model misspecification and a systematic failure to represent the future distribution.
1424:
922:
262:
1003:
1016:
312:(1997; ÂŁ90m loss) - incorrect model specification, "a naive volatility input in their systems", for interest rate options and swaptions.
1264:
Rantala, J. (2006). "On joint and separate history of probability, statistics and actuarial science". In Liksi; et al. (eds.).
441:
However, model risk is increasingly relevant in contexts other than financial securities valuation, including assigning consumer
1535:
Avellaneda, M.; Levy, A.; Parás, A. (1995). "Pricing and hedging derivative securities in markets with uncertain volatilities".
1030:
Avellaneda, M.; Levy, A.; Parás, A. (1995). "Pricing and hedging derivative securities in markets with uncertain volatilities".
1677:
1084:
Cont, Rama; Romain
Deguest (2013). "Equity Correlations Implied by Index Options: Estimation and Model Uncertainty Analysis".
1493:
1468:
1220:
1715:
Jokhadze, Valeriane; Schmidt, Wolfgang M. (2018). "Measuring model risk in financial risk management and pricing". SSRN.
1592:
Cont, R.; Deguest, R. (2013). "Equity
Correlations Implied by Index Options: Estimation and Model Uncertainty Analysis".
943:
840:
1797:
1250:
255:
376:
1821:
1666:
1273:
631:
examples of superposed model risk measures in the context of financial risk management and contingent claim pricing.
360:
780:
758:
396:
384:
810:
770:
537:
models that allow for a perfect fit of the term structure of the interest rates. In these models the current
248:
426:
Here, Rebonato (2002) defines model risk as "the risk of occurrence of a significant difference between the
1399:
1622:
1557:
1509:
Fender, Ingo; Kiff, John (2004). "CDO rating methodology: Some thoughts on model and its implications".
1309:
1004:
http://www.siiglobal.org/SII/WEB5/sii_files/Membership/PIFs/Risk/Model%20Risk%2024%2011%2009%20Final.pdf
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1840:
1435:
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699:
543:
1749:
1704:
1197:
1155:
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1175:
586:
317:
729:
Taleb wrote when describing why most new models that attempted to correct the inadequacies of the
32:
1845:
372:
364:
352:
332:
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1128:
891:
340:
289:
1346:
1113:
1736:
1518:
1184:
1142:
59:
958:
420:
325:
606:
8:
1169:
Frey, RĂĽdiger (2000). "Market
Illiquidity as a Source of Model Risk in Dynamic Hedging".
1757:
Lyons, T. J. (1995). "Uncertain volatility and the risk-free synthesis of derivatives".
1724:
1708:
1645:
1609:
1580:
1369:
1101:
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227:
82:
54:
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1097:
730:
293:
186:
64:
1686:
1613:
1584:
1373:
1105:
533:
Buraschi and
Corielli formalise the concept of 'time inconsistency' with regards to
1774:
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1716:
1637:
1601:
1572:
1544:
1361:
1324:
1093:
1070:
1066:
1039:
822:
673:
582:
517:
321:
191:
130:
1127:
Gennheimer, Heinrich (2002). "Model Risk in Copula Based
Default Pricing Models".
296:
instead of separate annuity yield-curves and zero-coupon curves for the resultant
775:
590:
522:
446:
416:
392:
356:
149:
107:
49:
757:
Fender and Kiff (2004) note that holding complex financial instruments, such as
1290:
926:
737:"Traders are not fooled by the Black–Scholes–Merton model. The existence of a '
556:
435:
301:
236:
201:
168:
163:
140:
121:
102:
87:
24:
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844:
1834:
1801:
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427:
297:
285:
177:
112:
92:
1236:
458:
Derman describes various types of model risk that arise from using a model:
1558:"Model Uncertainty and Its Impact on the Pricing of Derivative Instruments"
1347:"Model uncertainty and its impact on the pricing of derivative instruments"
581:
is therefore an important issue in the analysis of model risk in general."
442:
434:
instrument, and the price at which the same instrument is revealed to have
329:
211:
196:
135:
1812:
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets
826:
1720:
979:
746:
703:
602:
538:
388:
220:
97:
73:
40:
419:
to make decisions, originally and frequently in the context of valuing
206:
997:
534:
1623:"Robustness and sensitivity analysis of risk measurement procedures"
939:"National Australia Bank chief promises review as share price drops"
431:
415:
is the risk of loss resulting from using insufficiently accurate
408:
309:
670:
Considering simple cases and their solutions (model boundaries).
709:
Avoid letting small issues snowball into large issues later on.
559:) are more exposed to model uncertainty than index options.
1017:"Laughter in the Dark: The Problem of the Volatility Smile"
348:
959:"Recipe for Disaster: The Formula That Killed Wall Street"
1798:“Investment Model Validation - A Guide for Practitioners”
1703:
Board of Governors of the Federal Reserve System (2011).
643:
617:
912:
See "Chapter 14 - Model Risk" in Crouhy, Galai and Mark.
355:
had drastically under-estimated the risks of a profound
1386:
883:
689:
Disseminating the model outwards in an orderly manner.
351:(1998; required $ 3.65 billion in recapitalization) -
320:(1997; $ 83m loss) - a "systematic pricing bias" for
1452:
1416:
1008:
1461:
Dynamic Hedging: Managing Vanilla and Exotic Options
1423:
Kato, Toshiyasu; Yoshiba, Toshinao (December 2000).
1268:. University of Tampere, Finland. pp. 261–284.
719:
1620:
1534:
1029:
974:
972:
379:
interest rate model made inconsistent use of rates.
1809:
1484:Cherubini, Umberto; Lunga, Giovanni Della (2007).
1477:
1266:Festschrift for Tarmo Pukkila on his 60th Birthday
1083:
634:
1657:Crouhy, Michel; Galai, Dan; Mark, Robert (2000).
1380:
1120:
1832:
1307:
1056:
969:
546:: specification, estimation and implementation.
1714:
1705:"Supervisory Guidance on Model Risk Management"
1656:
1310:"Maxmin expected utility with non-unique prior"
1077:
1023:
343:(1997; ÂŁ15m loss) - mispriced currency options.
1483:
1204:
575:
256:
1788:Rebonato, R. (2001). "Managing Model Risk".
1621:Cont, R.; Deguest, R.; Scandolo, G. (2010).
1396:Leibnitz University Discussion Paper No. 409
1387:Sibbertsen; Stahl; Luedtke (November 2008).
511:
1591:
1422:
1340:
1338:
486:Use of inaccurate numerical approximations.
1508:
1126:
931:
923:"Oops! Bank Will Write Off $ 1.75 Billion"
612:
549:
263:
249:
1778:
1502:
1174:
1132:
1050:
1787:
1335:
951:
804:
802:
800:
771:Financial risk management § Banking
1263:
1257:
889:
811:"Interest rate model risk: An overview"
474:
328:swaptions which had been calibrated to
1833:
1675:
1288:
1014:
808:
644:Position limits and valuation reserves
618:Model averaging vs worst-case approach
1807:
1756:
1458:
1210:
797:
752:
715:Ongoing monitoring and against market
596:
528:
1555:
1344:
1168:
1162:
903:Evaluation of various finance models
661:
1308:Gilboa, I.; Schmeidler, D. (1989).
944:Australian Broadcasting Corporation
809:Gibson, et al. (Spring 1999).
13:
841:"Model Validation and Backtesting"
14:
1862:
1317:Journal of Mathematical Economics
733:model failed to become accepted:
720:Examples of model risk mitigation
680:
521:volatility uncertainty. See also
375:(2001; $ 2.2 Billion AUD loss) -
1606:10.1111/j.1467-9965.2011.00503.x
1577:10.1111/j.1467-9965.2006.00281.x
1366:10.1111/j.1467-9965.2006.00281.x
1098:10.1111/j.1467-9965.2011.00503.x
1059:Journal of Banking & Finance
1015:Derman, Emanuel (May 26, 2003).
31:
1301:
1282:
1251:"Ferret Out Spreadsheet Errors"
1243:
1229:
781:Statistical model specification
635:Quantifying model risk exposure
397:collateralized debt obligations
1071:10.1016/j.jbankfin.2005.02.002
921:Becky Gaylord (Sept. 8, 2001)
915:
906:
858:
833:
490:
470:Incorrect model specification.
461:
1:
1528:
1432:Monetary and Economic Studies
1289:Savage, Sam (November 2002).
656:
566:
1759:Applied Mathematical Finance
1537:Applied Mathematical Finance
1425:"Model Risk and Its Control"
1329:10.1016/0304-4068(89)90018-9
1215:. McGraw-Hill Professional.
1032:Applied Mathematical Finance
724:
667:Considering key assumptions.
601:Many models are built using
395:model misprices the risk of
274:
7:
1790:Handbook of Risk Management
899:New England Economic Review
764:
10:
1867:
890:Simmons, Katerina (1997).
693:
587:mortgage-backed securities
576:Illiquidity and model risk
506:
430:value of a complex and/or
385:2007–2008 financial crisis
288:(1970s; $ 70m loss) - for
1771:10.1080/13504869500000007
1642:10.1080/14697681003685597
1549:10.1080/13504869500000005
1044:10.1080/13504869500000005
512:Uncertainty on volatility
467:Inapplicability of model.
277:
1796:Joseph Simonian (2024).
1676:Derman, Emanuel (1996).
1237:"EuSpRIG Horror Stories"
1211:Black, Keith H. (2004).
866:"Controlling Model Risk"
791:
453:
447:prediction of fraudulent
361:insufficient data-window
318:Bank of Tokyo-Mitsubishi
1295:Harvard Business Review
613:Quantitative approaches
550:Correlation uncertainty
373:National Australia Bank
1808:Taleb, Nassim (2006).
1744:Cite journal requires
1685:. RISK. Archived from
1459:Taleb, Nassim (2010).
1389:"Measuring Model Risk"
1291:"The Flaw of Averages"
1192:Cite journal requires
1150:Cite journal requires
712:Independent validation
341:Barclays de Zoete Wedd
1213:Managing a Hedge Fund
827:10.21314/JOR.1999.009
1804:Research Foundation.
1721:10.2139/ssrn.3113139
1630:Quantitative Finance
1594:Mathematical Finance
1565:Mathematical Finance
1354:Mathematical Finance
1086:Mathematical Finance
965:. February 23, 2009.
496:Implementation risk.
475:Model implementation
436:traded in the market
421:financial securities
1792:. FT-Prentice Hall.
1463:. New York: Wiley.
1345:Cont, Rama (2006).
815:The Journal of Risk
686:Pride of ownership.
502:Calibration errors.
480:Programming errors.
387:– Over-reliance on
1780:10338.dmlcz/135679
1709:US Federal Reserve
1511:BIS Working Papers
1488:. Hoboken: Wiley.
1486:Structured Finance
753:Model risk premium
739:volatility surface
597:Spreadsheet Errors
529:Time inconsistency
228:Non-financial risk
83:Interest rate risk
55:Concentration risk
1841:Actuarial science
1556:Cont, R. (2006).
1495:978-0-470-02638-0
1470:978-0-471-35347-8
1222:978-0-07-143481-2
662:Theoretical basis
583:Convertible bonds
483:Technical errors.
405:
404:
273:
272:
187:Reputational risk
1858:
1851:Financial models
1827:
1815:
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1784:
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1506:
1500:
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1481:
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1447:
1446:
1440:
1434:. Archived from
1429:
1420:
1414:
1413:
1411:
1410:
1404:
1398:. Archived from
1393:
1384:
1378:
1377:
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1342:
1333:
1332:
1314:
1305:
1299:
1298:
1286:
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1254:
1253:. February 2004.
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902:
896:
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877:
868:. Archived from
862:
856:
855:
853:
852:
843:. Archived from
837:
831:
830:
806:
607:Spreadsheet risk
591:high-yield bonds
518:volatility smile
322:out-of-the-money
292:, used a single
275:
265:
258:
251:
192:Operational risk
131:Refinancing risk
35:
16:
15:
1866:
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1831:
1830:
1824:
1745:
1743:
1734:
1733:
1695:
1693:
1689:
1682:
1669:
1661:. McGraw-Hill.
1659:Risk Management
1625:
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1507:
1503:
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1134:10.1.1.139.2327
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1024:
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1002:
998:
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947:. 12 June 2023.
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544:risk management
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523:volatility risk
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493:
477:
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393:Gaussian copula
357:economic crisis
269:
150:Investment risk
108:Volatility risk
50:Settlement risk
12:
11:
5:
1864:
1854:
1853:
1848:
1846:Financial risk
1843:
1829:
1828:
1822:
1805:
1794:
1785:
1765:(2): 117–133.
1754:
1746:|journal=
1712:
1701:
1673:
1667:
1654:
1636:(6): 593–606.
1618:
1600:(3): 496–530.
1589:
1571:(3): 519–547.
1553:
1530:
1527:
1525:
1524:
1501:
1494:
1476:
1469:
1451:
1415:
1379:
1360:(3): 519–547.
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1300:
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1228:
1221:
1203:
1194:|journal=
1176:10.1.1.29.6703
1161:
1152:|journal=
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1092:(3): 496–530.
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927:New York Times
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557:rainbow option
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363:and a lack of
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169:Valuation risk
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141:Margining risk
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122:Liquidity risk
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60:Sovereign risk
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25:Financial risk
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1694:. Retrieved
1687:the original
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1543:(2): 73–88.
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1065:(11): 2883.
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1038:(2): 73–88.
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987:. Retrieved
980:"Model Risk"
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870:the original
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535:no-arbitrage
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499:Data issues.
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445:, real-time
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377:its Homeside
359:, due to an
330:at-the-money
279:
278:
212:Moral hazard
197:Country risk
158:
136:Deposit risk
65:Default risk
747:overfitting
704:backtesting
603:spreadsheet
539:yield curve
491:Model usage
462:Wrong model
389:David X. Li
353:risk models
304:securities.
221:Profit risk
98:Equity risk
74:Market risk
41:Credit risk
1835:Categories
1696:2008-12-01
1679:Model Risk
1529:References
1445:2009-02-15
1409:2014-03-10
1323:(2): 141.
876:2008-12-01
851:2008-12-01
657:Mitigation
567:Complexity
413:model risk
335:swaptions.
207:Legal risk
159:Model risk
1816:. Wiley.
1729:169594252
1650:158678050
1171:CiteSeerX
1129:CiteSeerX
725:Parsimony
674:Parsimony
294:par yield
1614:43322093
1585:16075069
1374:16075069
1106:43322093
901:: 17–28.
765:See also
432:illiquid
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1114:1592531
694:Testing
507:Sources
409:finance
333:vanilla
326:Bermuda
310:NatWest
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589:, and
417:models
1725:S2CID
1690:(PDF)
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1370:S2CID
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1102:S2CID
983:(pdf)
963:Wired
895:(PDF)
792:Notes
454:Types
1818:ISBN
1750:help
1663:ISBN
1515:SSRN
1490:ISBN
1465:ISBN
1270:ISBN
1217:ISBN
1198:help
1156:help
1110:SSRN
991:2013
759:CDOs
702:and
349:LTCM
324:and
300:and
1775:hdl
1767:doi
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