Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications

638 Pages·2016·9.277 MB·English

by  Longin, Francois(Editor)

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Extreme Events in Finance
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WileyHandbooksin
FINANCIAL ENGINEERING AND ECONOMETRICS
AdvisoryEditor
Ruey S. Tsay
TheUniversityofChicagoBoothSchoolofBusiness,USA
Acompletelistofthetitlesinthisseriesappearsattheendofthisvolume.
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Extreme Events in Finance
A Handbook of Extreme Value
Theory and its Applications
Edited by
FRANÇOIS LONGIN
DepartmentofFinance,
ESSECBusinessSchool,
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Paris,France
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Copyright©2017byJohnWiley&Sons,Inc.Allrightsreserved
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LibraryofCongressCataloging-in-PublicationData:
Names:Longin,FrançoisMichel,1968-editor.
Title:Extremeeventsinfinance:ahandbookofextremevaluetheoryandits
applications/editedbyFrançoisLongin.
Description:Hoboken:Wiley,2017.|Series:Wileyhandbooksinfinancial
engineeringandeconometrics|Includesbibliographicalreferencesand
index.
Identifiers:LCCN2016004187|ISBN9781118650196(hardback)|ISBN
9781118650202(epub)
Subjects:LCSH:Finance–Mathematicalmodels.|Extremevalue
theory–Mathematicalmodels.|BISAC:BUSINESS&ECONOMICS/Insurance/
RiskAssessment&Management.
Classification:LCCHG106.E982016|DDC332.01/5195–dc23LCrecordavailableat
http://lccn.loc.gov/2016004187
CoverimagecourtesyofiStockphoto©Nikada
Typesetin10/12ptTimesLTStdbySPiGlobal,Chennai,India
PrintedintheUnitedStatesofAmerica
10987654321
12017
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Contents
AbouttheEditor xiii
AbouttheContributors xv
1 Introduction 1
FrançoisLongin
1.1 Extremes 1
1.2 History 2
1.3 Extremevaluetheory 2
1.4 Statisticalestimationofextremes 2
1.5 Applicationsinfinance 4
1.6 Practitioners’pointsofview 6
(cid:2) 1.7 Abroaderviewonmodelingextremes 6 (cid:2)
1.8 Finalwords 7
1.9 Thankyounote 7
References 8
2 ExtremesUnderDependence—HistoricalDevelopmentand
ParallelswithCentralLimitTheory 11
M.R.Leadbetter
2.1 Introduction 11
2.2 Classical(I.I.D.)centrallimitandextremevaluetheories 12
2.3 Exceedancesoflevels,kthlargestvalues 14
2.4 CLTandEVTforstationarysequences,bernstein’sblocks,
andstrongmixing 15
2.5 WeakdistributionalmixingforEVT,D(u ),extremalindex 18
n
2.6 Pointprocessoflevelexceedances 19
2.7 Continuousparameterextremes 20
References 22
3 TheExtremeValueProbleminFinance:Comparingthe
PragmaticProgramwiththeMandelbrotProgram 25
ChristianWalter
3.1 Theextremevaluepuzzleinfinancialmodeling 25
3.2 Thesatoclassificationandthetwoprograms 28
3.3 Mandelbrot’sprogram:Afractalapproach 34
v
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vi Contents
3.4 ThePragmaticProgram:Adata-drivenapproach 39
3.5 Conclusion 47
Acknowledgments 48
References 48
4 ExtremeValueTheory:AnIntroductoryOverview 53
IsabelFragaAlvesandCláudiaNeves
4.1 Introduction 53
4.2 Univariatecase 56
4.3 Multivariatecase:Somehighlights 84
Furtherreading 90
Acknowledgments 90
References 90
5 EstimationoftheExtremeValueIndex 97
BeirlantJ.,HerrmannK.,andTeugelsJ.L.
5.1 Introduction 97
5.2 Themainlimittheorembehindextremevaluetheory 98
5.3 Characterizationsofthemax-domainsofattractionand
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5.4 Consistencyandasymptoticnormalityoftheestimators 103
5.5 Second-orderreduced-biasestimation 104
5.6 Casestudy 106
5.7 Othertopicsandcomments 108
References 111
6 BootstrapMethodsinStatisticsofExtremes 117
M.IvetteGomes,FredericoCaeiro,LígiaHenriques-Rodrigues,
andB.G.Manjunath
6.1 Introduction 117
6.2 AfewdetailsonEVT 119
6.3 Thebootstrapmethodologyinstatisticsofunivariateextremes 127
6.4 Applicationstosimulateddata 133
6.5 Concludingremarks 133
Acknowledgments 135
References 135
7 ExtremeValuesStatisticsforMarkovChainswithApplications
toFinanceandInsurance 139
PatriceBertail,StéphanClémençon,andCharlesTillier
7.1 Introduction 139
7.2 Onthe(pseudo)regenerativeapproachformarkoviandata 141
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Contents vii
7.3 Preliminaryresults 151
7.4 Regeneration-basedstatisticalmethodsforextremalevents 154
7.5 Theextremalindex 156
7.6 Theregeneration-basedhillestimator 159
7.7 Applicationstoruintheoryandfinancialtimeseries 161
7.8 AnapplicationtotheCAC40 165
7.9 Conclusion 167
References 167
8 LévyProcessesandExtremeValueTheory 171
OlivierLeCourtoisandChristianWalter
8.1 Introduction 171
8.2 Extremevaluetheory 173
8.3 InfinitedivisibilityandLévyprocesses 178
8.4 Heavy-tailedLévyprocesses 182
8.5 Semi-heavy-tailedLévyprocesses 184
8.6 Lévyprocessesandextremevalues 187
8.7 Conclusion 192
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References 192
9 StatisticsofExtremes:ChallengesandOpportunities 195
M.deCarvalho
9.1 Introduction 195
9.2 Statisticsofbivariateextremes 196
9.3 Modelsbasedonfamiliesoftiltedmeasures 204
9.4 Miscellanea 209
References 211
10 MeasuresofFinancialRisk 215
S.Y.Novak
10.1 Introduction 215
10.2 Traditionalmeasuresofrisk 215
10.3 Riskestimation 218
10.4 “Technicalanalysis”offinancialdata 222
10.5 Dynamicriskmeasurement 226
10.6 Openproblemsandfurtherresearch 234
10.7 Conclusion 235
Acknowledgment 235
References 235
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viii Contents
11 OntheEstimationoftheDistributionofAggregated
Heavy-TailedRisks:ApplicationtoRiskMeasures 239
MarieKratz
11.1 Introduction 239
11.2 Abriefreviewofexistingmethods 245
11.3 Newapproaches:Mixedlimittheorems 247
11.4 Applicationtoriskmeasuresandcomparison 269
11.5 Conclusion 277
References 279
12 EstimationMethodsforValueatRisk 283
SaraleesNadarajahandStephenChan
12.1 Introduction 283
12.2 Generalproperties 289
12.3 Parametricmethods 300
12.4 Nonparametricmethods 326
12.5 Semiparametricmethods 332
12.6 Computersoftware 344
12.7 Conclusions 347
Acknowledgment 347
References 347
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13 ComparingTailRiskandSystemicRiskProfilesforDifferent
TypesofU.S.FinancialInstitutions 357
StefanStraetmansandThanhThiHuyenDinh
13.1 Introduction 357
13.2 Tailriskandsystemicriskindicators 361
13.3 Tailriskandsystemicriskestimation 364
13.4 Empiricalresults 368
13.5 Conclusions 381
References 382
14 ExtremeValueTheoryandCreditSpreads 391
WesleyPhoa
14.1 Preliminaries 391
14.2 Tailbehaviorofcreditmarkets 394
14.3 Somemultivariateanalysis 398
14.4 Approximatingvalueatriskforcreditportfolios 401
14.5 Otherdirections 403
References 404
15 ExtremeValueTheoryandRiskManagementin
ElectricityMarkets 405
KamFongChanandPhilipGray
15.1 Introduction 405
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