金融衍生工具讲义(香港中文大学 何佳)

TheCurvatureandSlopeinCreditSpreadTermStructureCurveJiaHeWenweiHuChineseUniversityofHongKong2Motivationrisk-freeInterestratetermstructuredynamicsofexpectedfuture...pricing...riskyYY*CreditSpreadexpectedfuturecreditrisk(dt,lt)Creditspreadtermstructuredynamicsofexpectedfuture…pricing...Pricingcreditrisk,credit-riskyassets,creditderivativesCurveshapecreditquality,creditcycle,businesscycleCreditriskmanagement(e.g.buyaputoptiononitsowncreditspreadtohedge)AsiafinancialcrisisUShighyieldmarket3Example:ARiskyBondRatedBBHowmuchwillitbeworthnextyear?HowmuchwillIlose,ifnextyearisbad?AAAAAc+1AccccBBBBBBBBCCCCCCD44433322211)1(1)1()1(1srcsrcsrcsrccp4Example:CreditOptionSpreadShighSlowTime5Motivationrisk-freeInterestratetermstructuredynamicsofexpectedfuture...pricing...riskyYY*CreditSpreadexpectedfuturecreditrisk(dt,lt)Creditspreadtermstructuredynamicsofexpectedfuture…pricing...Pricingcreditrisk,credit-riskyassets,creditderivativesCurveshapecreditquality,creditcycle,businesscycleCreditriskmanagement(e.g.buyaputoptiononitsowncreditspreadtohedge)AsiafinancialcrisisUShighyieldmarket6TheoreticalEmpiricalSlopes:InvestmentSpeculativeUpwardDownwardUpwardDifferentCurvaturesSlighthumpNoproofNocomplete&strictexplorationNoappropriateapproachSlope-ratingrelationshipNoneNoneCurvature-ratingrelationshipNoneNoneLiteraturesReview-PriorResults7LiteraturesReview-PriorResultsHelwage&Turner(1999):BondpoolingsampleselectionbiasDifferentfirmsdifferentcreditqualitySaferfirmsissuelongtermbondsspreaddeclineControlcreditqualitybondgrouping（samerating，sameissuer，sameissuedate）Speculative：upwardsloping8TheoreticalEmpiricalSlopes:InvestmentSpeculativeUpwardDownwardUpwardDifferentCurvaturesSlighthumpNoproofNocomplete&strictexplorationNoappropriateapproachSlope-ratingrelationshipNoneNoneCurvature-ratingrelationshipNoneNoneLiteraturesReview-PriorResults9EmpiricalSlopes:InvestmentSpeculativeUpUp,DownCurvaturesExtensiveexplorationBondpairapproachSlope-ratingrelationshipYesYesCurvature-ratingrelationshipYesYesOurContributions10Curvature?11ArgumentLINEARTermStructureCurvesNOTApplicabletoMiddleRatedFirms12LINEARTermStructureCurveNOTApplicabletoMiddleRatedFirms-fromslopeexplanationupwardcurrentbestbestfirmStdowncurrentworstworstfirmSt(ifundefault)??bestworst?St?middlegradedfirm?13•defaultspread•downupupwardatfirst•reachpeakdownward02468101214AAAABBCCC-Cdefaultup-gradedown-gradeLINEARTermStructureCurveNOTApplicabletoMiddleRatedFirms-fromhistoricaldata(1920-1996)(ifundefault)14•Ratingcriteriastringent•Betterfirmsfirstrating•FirmsaskforratingattheirbestperiodsLINEARTermStructureCurveNOTApplicabletoMiddleRatedFirms-whydownup?15OurNewFindings•middlegradedbonds•highestratedbonds•lowestratedbonds•relationshipamongspreadcurvesSpreadLowestgradedeterioratedmiddleimprovedHighestgradeMaturity16DataDescription•LehmanBrothersFixedIncomeDatabase(USbonds)•Jan.1993-Jan.1997•Havingrating,traderquotedprices,yieldinformation•Maturity1year•Embeddedoptions:•Pooledbondssample(pre-grouped)(withsamerating)•Groupedbondssample(withsamerating,sameissuer,sametradingdate)17OurResearchWork•Directobservationsforpooledbonds•Directobservationsforgroupedbonds•Statisticaltestsforcurvature&slope•Develop:BondPairApproach18DetailsAboutOurWork…...19DirectObservations-forsameratingbondsInvestmentGradeAAA+20DirectObservations-forsameratingbondsInvestmentGradeAAA21DirectObservations-forsameratingbondsInvestmentGradeAA22DirectObservations-forsameratingbondsInvestmentGradeA23DirectObservations-forsameratingbondsInvestmentGradeBBB24DirectObservations-forsameratingbondsInvestmentGradeBB25DirectObservations-forsameratingbondsInvestmentGradeB26DirectObservations-forsameratingbondsSpeculativeGradeCCC27DirectObservations-forsameratingbondsSpeculativeGradeCC28DirectObservations-forsameratingbondsSpeculativeGradeC29DirectObservations-forsameratingbondsInvestmentGradesSpeculativeGrades30DirectObservations-forindividualfirmbonds•Bondpoolingsampleselectionbias•Bondgroupingsamerating,sameissuer,sametradingdate,butnosameissuedate31DirectObservations-forindividualfirmbonds(BB)SpreadCurveShapeGroupMaturity(year)1-22-55-1010-1515-2020-2525-30Total1-301005321372652221275000533522472001199151157148120228471421101421173039121111219836105179211825154342101225220312172211537328121927725Total6483639410813016291132DirectObservations-forindividualfirmbonds(BB)SpreadCurveShapeGroupMaturity(year)1-22-55-1010-1515-2020-2525-30Total1-30GLOBALSLOPE0**Flat0.000.100.090.050.020.000.010.051**Upward0.830.670.560.700.810.780.900.702**Downward0.170.230.350.240.170.220.090.24CURVATURE*00Linear0.831.000.740.490.600.210.06↓0.52*1*Concave0.170.000.120.360.280.620.91↑0.37*2*Convex0.000.000.130.150.120.170.02↓0.11*11Hump0.000.000.080.120.120.390.67↑0.23KEYRATIOSUp/Down15.002.911.602.874.893.6410.43↑2.89Concave/Convex10.922.432.313.6837.00↑3.32Hump/Concave→10.000.640.320.430.630.74↑0.6333DirectObservations-forindividualfirmbonds(B)SpreadCurveShapeGroupMaturity(ye