【精品】the curvature and slope in credit spread term structure curve(可编辑.ppt
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1、The Curvature and Slope in Credit Spread Term Structure CurveMotivationriskfreeInterestratetermstructuredynamicsofexpectedfuture.pricing.riskyYY*CreditSpreadexpectedfuturecreditrisk(dt,lt)Creditspreadtermstructuredynamicsofexpectedfuturepricing.Pricingcreditrisk,creditriskyassets,creditderivativesCu
2、rveshapecreditquality,creditcycle,businesscycleCreditriskmanagement(e.g.buyaputoptiononitsowncreditspreadtohedge)AsiafinancialcrisisUShighyieldmarket2Example:A Risky Bond Rated BBHowmuchwillitbeworthnextyear?HowmuchwillIlose,ifnextyearisbad?AAAAAc+1AccccBBBBBBBBCCCCCCD3Example:Credit OptionSpreadShi
3、ghSlowTime4MotivationriskfreeInterestratetermstructuredynamicsofexpectedfuture.pricing.riskyYY*CreditSpreadexpectedfuturecreditrisk(dt,lt)Creditspreadtermstructuredynamicsofexpectedfuturepricing.Pricingcreditrisk,creditriskyassets,creditderivativesCurveshapecreditquality,creditcycle,businesscycleCre
4、ditriskmanagement(e.g.buyaputoptiononitsowncreditspreadtohedge)AsiafinancialcrisisUShighyieldmarket5Literatures Review-Prior Results8Our Contributions9Curvature?10Argument LINEAR Term Structure Curves NOT Applicable to Middle Rated Firms 11LINEAR Term Structure Curve NOT Applicable to Middle Rated F
5、irms-from slope explanationupwardcurrentbest bestfirmStdowncurrentworstworstfirm St(ifundefault)?bestworst?St?middlegradedfirm?12defaultspreaddownupupwardatfirstreachpeakdownwardLINEAR Term Structure Curve NOT Applicable to Middle Rated Firms-from historical data(1920-1996)(ifundefault)13Ratingcrite
6、riastringentBetterfirmsfirstratingFirmsaskforratingattheirbestperiodsLINEAR Term Structure Curve NOT Applicable to Middle Rated Firms-why downup?14Our New Findingsmiddlegradedbondshighestratedbondslowestratedbondsrelationshipamongspreadcurves15Data Description LehmanBrothersFixedIncomeDatabase(USbon
7、ds)Jan.1993Jan.1997Havingrating,traderquotedprices,yieldinformationMaturity1yearEmbeddedoptions:Pooledbondssample(pregrouped)(withsamerating)Groupedbondssample(withsamerating,sameissuer,sametradingdate)16Our Research Work DirectobservationsforpooledbondsDirectobservationsforgroupedbondsStatisticalte
8、stsforcurvature&slopeDevelop:Bond Pair Approach17DetailsAboutOurWork.18Direct Observations-for same rating bonds InvestmentGradeAAA+19Direct Observations-for same rating bonds InvestmentGradeAAA20Direct Observations-for same rating bonds InvestmentGradeAA21Direct Observations-for same rating bonds I
9、nvestmentGradeA22Direct Observations-for same rating bonds InvestmentGradeBBB23Direct Observations-for same rating bonds InvestmentGradeBB24Direct Observations-for same rating bonds InvestmentGradeB25Direct Observations-for same rating bonds SpeculativeGradeCCC26Direct Observations-for same rating b
10、onds SpeculativeGradeCC27Direct Observations-for same rating bonds SpeculativeGradeC28Direct Observations-for same rating bondsInvestmentGradesSpeculativeGrades29Direct Observations-for individual firm bondsBondpoolingsampleselectionbiasBondgroupingsamerating,sameissuer,sametradingdate,butnosameissu
11、edate30Direct Observations-for individual firm bonds(BB)31Direct Observations-for individual firm bonds(BB)32Direct Observations-for individual firm bonds(B)33Direct Observations-for individual firm bonds(B)34Direct Observations-for individual firm bonds(CCC)35Direct Observations-for individual firm
12、 bonds(CCC)36Observationalresultsareaffectedbymaturity!ObservationalError?37Observational Errors-caused by group size38Observational Errors-caused by group maturity39CausedbygroupsizeCausedbygroupmaturityObservational Errors Explanation40Include?Exclude?41Statistical Tests for Slopes,Curvatures,and
13、Peak Points ExistenceBondPairApproachsegmentslopescurvatureincludeallfirmssamplebiasMedianStatisticsSignTest&SignRankTestWilcoxonComparisonTest42Statistical Tests for Slopes,Curvatures,andPeak Points Existence-median statisticsGeneralSlopesSegmentSlopes(curvature)43SignTest&SignRankTestWilcoxonCompa
14、risonTestStatistical Tests for Slopes,Curvatures,andPeak Points Existence-other tests44Statistical Tests for Peak Points Position 45EmbeddedOptionEffectBondGroupingEffectLiquidityEffectRobustness of Results46GeneralSlopesSegmentSlopes(curvature)Robustness of Results-embedded option effect47Robustnes
15、s of Results-bond grouping effect48GeneralSlopesSegmentSlopes(curvature)Robustness of Results-liquidity effect49Conclusionmiddlegradedbondshighestratedbondslowestratedbondsrelationshipamongspreadcurves(slp&cur)bondpairapproach50ImprovementofCreditMetricsTimeVaryingCreditSpreadCurvesandRatingMigratio
16、nsDeterminantsofCreditSpreadChangesMultiStatesPricingModelforCreditRiskMarketRatingAnObjectiveCreditRatingMethodAn Empirical Model for the Credit Risk TermStructureBasedonNewEvidenceFurther Research51BasicconceptsWhatisaderivative?ContractAderivativeisacontractbetweentwopartiesthatspecifiescondition
17、sinparticular,datesandtheresultingvalueofunderlyingvariablesunderwhichpaymentsorpayoffsaretobemadebetweentheparties.Example1:Socialsecurityisaderivativewhichrequiresaseriesofpaymentsfromanindividualtothegovernmentbeforeage65,andpayoffsafterage65fromthegovernmenttotheindividualaslongastheindividualre
18、mainsalive.Example2:Earthquakeinsuranceisaderivativeinwhichanindividualmakesregularannualpaymentsinexchangeforapotentiallymuchlargerpayofffromtheinsurancecompanyshouldanearthquakedestroyhisproperty.Derivativeisalsoknownascontingentclaimssincetheirpayoffsarecontingentupontheoutcomeofunderlyingvariabl
19、es.PayofftableEarthquakeinsurancepolicyRichterScaleDamagePayoff04.95.05.45.55.96.06.97.08.9NoneSlightSmallMediumLarge$075010,00025,00050,000SubjectiveprobabilityRichterScaleSubjectiveprobability04.95.05.45.55.96.06.97.085%1031.50.5%StatisticsofpayoffPayofffrominsurance(X1,X2,Xn)Subjectiveprobabiliti
20、es(Q1,Q2,Qn)Expectedpayoff,EX=Q1X1+Q2X2+QnXnVarianceofpayoff,Var(X)=Q1X1E(X)2+Q2X2E(X)2+QnXnE(X)2Covarianceofpayoff,Cov(X,Y)=Q1X1E(X)Y1E(Y)+Q2X2E(X)Y2E(Y)+QnXnE(X)YnE(Y)Inourinsuranceexample,E(X)=1,000,Var(X)23,931,250,Std=4,892.InsurancepremiumRiskfreerateis5%.Forthegivenexpectedvalueayearformnow,h
21、owmuchareyouwillingtopaytobytheinsurance?1,000?1,000/1.05=952.38,adjustfortimevalueofmoney?Peopleareriskaverse,theywouldwanttopaymore,thepremium!RiskaversionAnotherdollarwhenyouarealreadyrichissimplynotasvaluabletoyou(intermsofyourwelfareorutility)asanextradollarwhenyouarepoor.SayyourentirewealthisH
22、KD1,000,000.Takingtheextremecase,thechanceofmakingaprofitofanother1milliondollarsisnotworthitifitcomeswithanequalchanceoflosing1milliondollars.Riskneutral(riskadjusted)probabilitiesAverysimplewaytoadjustforriskaversionistoweightdollarslessthanwehavein“rich”statesandmorethanwehavein“poor”states.Riskn
23、eutralprobability=subjectiveprobability*riskaversionadjustmentTheexpectedvalueunderRiskneutralprobability=1,160Homeownerspresentvalue:1,160/1.05=1,104.76RichterScalePayoffSubjectiveprobabilityRiskaversionadjustmentRiskneutralprobabilityRiskneutralprobability*payoff04.95.05.45.55.96.06.97.08.9$075010
24、,00025,00050,00085%1031.50.5%.9939.99761.04721.14301.2787.845.100.031.017.007075310425350Earthquakeinsurance(allriskdiversifiablefrominsurancecompanyside)Eventhroughthehomeowneriswillingtopayapremiumashighas1,104.76,theinsurancecompanyiswillingtosellthepolicyforalower952.38premium.Competitionamongin
25、surancecompaniesservestodrivethepremiumdownto952.38.Sotheinsuranceisagooddealforthehomeowner!Thereasonwhytheinsurancecompanyiscontenttocharge952.38isthat,bysellingmanypoliciesindifferentpartsofthecountry,itcandiversifyawayalmostallitsriskunlikethehomeownerwhohasonehouse.Theinsurancecompanycanthenact
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