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1、AppliedQuantitativeFinanceWolfgangH•ardleTorstenKleinowGerhardStahlIncooperationwithG•okhanAydnl,OliverJimBlaskowitz,SongXiChen,MatthiasFengler,J•urgenFranke,ChristophFrisch,HelmutHerwartz,HarrietHolzberger,SteH•ose,StefanHuschens,KimHuynh,StefanR.Jaschke,YuzeJiangPierreKervella,R•ud
2、igerKiesel,GermarKn•ochlein,SvenKnoth,JensL•ussem,DaniloMercurio,MarleneM•uller,J•ornRank,PeterSchmidt,RainerSchulz,J•urgenSchumacher,ThomasSiegl,RobertWania,AxelWerwatz,JunZhengJune20,2002ContentsPrefacexvContributorsxixFrequentlyUsedNotationxxiIValueatRisk11ApproximatingValueatRiskinC
3、onditionalGaussianModels3StefanR.JaschkeandYuzeJiang1.1Introduction.............................31.1.1ThePracticalNeed.....................31.1.2StatisticalModelingforVaR...............41.1.3VaRApproximations....................61.1.4ProsandConsofDelta-GammaApproximations....71.2General
4、PropertiesofDelta-Gamma-NormalModels......81.3Cornish-FisherApproximations..................121.3.1Derivation..........................121.3.2Properties..........................151.4FourierInversion..........................16ivContents1.4.1ErrorAnalysis.......................161.4.2Ta
5、ilBehavior........................201.4.3InversionofthecdfminustheGaussianApproximation211.5VarianceReductionTechniquesinMonte-CarloSimulation...241.5.1Monte-CarloSamplingMethod..............241.5.2PartialMonte-CarlowithImportanceSampling.....281.5.3XploReExamples.....................30
6、2ApplicationsofCopulasfortheCalculationofValue-at-Risk35J•ornRankandThomasSiegl2.1Copulas...............................362.1.1De nition..........................362.1.2Sklar'sTheorem......................372.1.3ExamplesofCopulas....................372.1.4FurtherImportantPropertiesofCop
7、ulas........392.2ComputingValue-at-RiskwithCopulas.............402.2.1SelectingtheMarginalDistributions...........402.2.2SelectingaCopula.....................412.2.3EstimatingtheCopulaParameters............412.2.4GeneratingScenarios-MonteCarloValue-at-Risk...432.3Examples......
