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1、AppliedQuantitativeFinanceWolfgangH?ardleTorstenKleinowGerhardStahlIncooperationwithG?okhanAydnl,OliverJimBlaskowitz,SongXiChen,MatthiasFengler,J?urgenFranke,ChristophFrisch,HelmutHerwartz,HarrietHolzberger,SteH?ose,StefanHuschens,KimHuynh,StefanR.Jaschke,YuzeJiangPierreKervella,R?udigerKie
2、sel,GermarKn?ochlein,SvenKnoth,JensL?ussem,DaniloMercurio,MarleneM?uller,J?ornRank,PeterSchmidt,RainerSchulz,J?urgenSchumacher,ThomasSiegl,RobertWania,AxelWerwatz,JunZhengJune20,2002ContentsPrefacexvContributorsxixFrequentlyUsedNotationxxiIValueatRisk11ApproximatingValueatRiskinConditionalGaus
3、sianModels3StefanR.JaschkeandYuzeJiang1.1Introduction.............................31.1.1ThePracticalNeed.....................31.1.2StatisticalModelingforVaR...............41.1.3VaRApproximations....................61.1.4ProsandConsofDelta-GammaApproximations....71.2GeneralPropertiesofDelta-Gam
4、ma-NormalModels......81.3Cornish-FisherApproximations..................121.3.1Derivation..........................121.3.2Properties..........................151.4FourierInversion..........................16ivContents1.4.1ErrorAnalysis.......................161.4.2TailBehavior..................
5、......201.4.3InversionofthecdfminustheGaussianApproximation211.5VarianceReductionTechniquesinMonte-CarloSimulation...241.5.1Monte-CarloSamplingMethod..............241.5.2PartialMonte-CarlowithImportanceSampling.....281.5.3XploReExamples.....................302ApplicationsofCopulasfortheCalcula
6、tionofValue-at-Risk35J?ornRankandThomasSiegl2.1Copulas...............................362.1.1De nition..........................362.1.2Sklar'sTheorem......................372.1.3ExamplesofCopulas....................372.1.4FurtherImportantPropertiesofCopulas........392.2ComputingValue-at-Riskwit
7、hCopulas.............402.2.1SelectingtheMarginalDistributions...........402.2.2SelectingaCopula.....................412.2.3EstimatingtheCopulaParameters............412.2.4GeneratingScenarios-MonteCarloValue-at-Risk...432.3Examples......
