Credit_Risk_Modelling

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1、CREDITRISKMODELINGTomaszR.BieleckiDepartmentofAppliedMathematicsIllinoisInstituteofTechnologyChicago,IL60616,USAMoniqueJeanblancD¶epartementdeMath¶ematiquesUniversit¶ed'EvryVald'Essonne¶91025EvryCedex,France¶MarekRutkowskiSchoolofMathematicsandStatisticsUniver

2、sityofNewSouthWalesSydney,NSW2052,AustraliaCenterfortheStudyofFinanceandInsuranceOsakaUniversity,Osaka,Japan2Contents1StructuralApproach91.1NotationandDe¯nitions..................................91.1.1DefaultableClaims.................................91.1.2Ris

3、k-NeutralValuationFormula.........................101.1.3DefaultableZero-CouponBond..........................111.2Merton'sModel.......................................121.3FirstPassageTimes....................................151.3.1DistributionoftheFirstPassage

4、Time......................151.3.2JointDistributionofYand¿...........................181.4BlackandCoxModel...................................211.4.1BondValuation...................................221.4.2BlackandCoxFormula..............................231.4.3Cor

5、porateCouponBond..............................271.4.4OptimalCapitalStructure.............................291.5ExtensionsoftheBlackandCoxModel.........................301.5.1StochasticInterestRates.............................311.6RandomBarrier.................

6、.....................331.6.1IndependentBarrier................................332HazardFunctionApproach352.1ElementaryMarketModel.................................352.1.1HazardFunctionandHazardRate........................362.1.2DefaultableBondwithRecoveryatMatu

7、rity..................372.1.3DefaultableBondwithRecoveryatDefault...................402.2MartingaleApproach....................................412.2.1ConditionalExpectations.............................412.2.2MartingalesAssociatedwithDefaultTime...............

8、.....422.2.3PredictableRepresentationTheorem.......................462.2.4Girsanov'sTheorem................................482.2.5RangeofArbitragePrices............................