FRM一级强化段金融市场（标准版）

FinancialProductsFRM一级培训讲义-强化班tⅠSessionContentSession1FoundationsRiskManagementSession2QuantitativeAnalysis20203030Session3FinancialandProductsSession4andRiskModels2-123Framework•••Ratesy••••Forwardand•••Management3-1231:Rates123..Compounding.SpotandForward4-123CommonMarketyTheonyandybonds.ythathighlythatgovernmentacountrydefaultissueditsown•ynotbecauseusuallyartificially,duethefollowingtwoBankscapitalfortheirypositions.•Intheygettax5-123CommonLIBORLIBORthecosts18highlyRatesInathebetweensellingprice(today)thepriceorcalledtheSOFRbeginphasingoutLiborwithaonactualtransactions。U.S.hastheusetheOvernightFinancing(SOFR)Risk-Freeatwhichpricedovernightusingovernightindexedswaps.6-123CompoundingFrequenciesSupposeaccountthesimpleandthenthatmoneyalsoAssumingRCthewithcontinuouscompounding.Rmthewithcompoundingannum)Tthenumberyears.mTRmmRTFV=PV1+FV=PVeCm1Tm2TmTR1m1R2m2RPV1+m=PVeRTPV1+=PV1+Cm7-123ForwardSpotAt-periodspotor,justonetime.Forwardaperiodbythespotcurve.T1(T−T)T21+R11+F=1+R221RT−RT2211RT×eFT2−T1=R2T2→F=e112−T18-1232:y1.yInstruments9-123yInstrumentsyBillsAshort-termobligationwithamaturityoneorless.onadiscount.yNotesandyBondsBondwithamaturityBondstypicallymaturitiesyearsyButthewillcoupon-bearingyinstrumentsyBonds.Both.QuotedPrice：Dollarsandthirty-secondsawithface$100ySTRIPSand10-123yInstrumentsCleanPriceacouponincludinganyaccruedfollowingeachcouponthepricewillequalthedirty.DirtyPriceApricingquotetheacouponthecashincludingaccruingonthenextcoupon.dirty=+AccruedandDayCountConventionsybonds:actual/actualCorporateandbonds:30/360Moneyinstrumentsyactual/36011-123yInstrumentsExampleSupposea1000UScorporatebondasemi-annualcouponJanuary1andJuly1.April1,2005,andthebond1,2015.the(full)pricethisyield8theflatthebond.TimeMar1st1stMay1stJune1stJuly1stdirty1155.301162.871170.501178.181185.901138.631137.871137.171136.511135.9012-1233:CorporateBond123.Bond.ClassificationBonds.BondRisk13-123BondIndentureContractcontainscorporatebondissuerpromisesinvestors’outcorporatebondholders’CorporateAinstitutionthethethattheissuertheindentures.Itsdutiestheindenturestheundernothose.theindenturethattrusteetheforsothat,not持续更新通知微：xuebajun888s14-123ClassificationBondsFloating-RateBondsZero-CouponBondsCollateralMortgageBondsBondsEquipmentCertificatesBonds(includingGuaranteedBondsHigh-YieldBond15-123RiskRiskmanythatadverselyaffectbonds,suchnaturaldisasters.typeriskcalledeventrisk.importanttyperisktheriska.CreditRiskCreditDefaultRisk:Riskabondbeunablefinancialobligations.CreditSpreadRisk:Riskloss.16-1231Eachthefollowingtrueaboutthecorporateacorporatebondissuanceexcept:A.bondholders.actsafiduciaryforinvestorswhoownbondissue.C.atthetimeissue,authenticatetheissued(i.e.,trackthebondssole)andthattheydoexceedtheamountauthorizedtheIfacorporateissuerfailstoorprincipal,theadefaultandsuchactionasmaynecessarytherightsbondholders.Answer:A17-1231:Introduction123.Introduction.and.CentralCounterparty18-123IntroductionDerivativesAninstrumentwhoseunderlyingassets.BasicDerivativesForwardandFuturesbuy/sellassettimeforcertainForward:theover-the-counterFutures:andon.SwapAforwardcontracts.cashflowsonperiodsettlement.Optionholderthe(butnotobligation)buy/sellacertain19-123IntroductionLinearandNon-LinearDerivativesbeandnonlinearthetheunderlyingassets.ForforwardcontractsOptions,othernonlinear,is,abetweenthetheoptionandthetheunderlyingasset.20-123Over-the-CounterandOver-the-CounterCustomizedwithcounterparty(DefaultRisk)ahouseNottradeacentrallocationaphysicalsmall21-123MarketAnatradecontractsbymembersso-calledcentralcounterpartiestheircounterpartiesmembers.Anotherusingamemberscloseoutpositions.Anothernetting.Nettingoperationshortandpositionsaparticularcontractothe22-123Marketmembersby.cashoroneanotherforagainstcounterpartydefault.MarginInitialMarginInaddition,submitadefaultfundaIftheinitialnotalossesduringadefault,contributionsbeusedtheIftheseinsufficient,bythefundsothermembers.23-123MarketMaintenanceMarginSotalkingaccountsandtheirmembers.atradercontactsatothatbethetradersandandmembers.ItcontainsforInwiththetheaccountthethemustadditionalaccountIfnotadditionalatradethecloseouttheposition.24-123CounterpartyOperationmargindailytotheportfolio.Whenadefaults,theholdsauction,invitingothermembersforthetransaction.chooseupThistheclosetransactionsaandthedefaultingpartyathatcausessomelossthenon-defaultinginitialbebycalculatedusingdata.theinitialthethethebeIfthatenough,contributionsothermembersused.25-123CounterpartyandDisadvantagesCentralClearingEasyexitLossmutualizationlossmechanismnetting,resolution)liquidityFormulationdocumentsfortransactions.DisadvantagesCentralClearingMoralAdverseselectionriskbymembersonfundscontribution26-1232:ForwardandFutures123456.Forward..Forwardand...27-123ForwardForwardAgreementAforward(FRA)thatacertainwillacertainduringacertaintimeThelocksaandthelocksaSettlement:thethe.thebeginningperiodbytheFRAbyconvention.forpartywhoandortheothersidethetransactionis:R−RKτL+RτRK−RτL1+Rτor1RRKtheLtheandτthelengththetimehorizon.28-123Forwardpartywhoandorothersidethetransactionis:R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oticOptions72-123PropertiesBasicsCallandPutOptionsandOptionMoneynessInmoney:wouldapositivemoney:wouldnoOutmoney:wouldalossIntrinsicandTimeIntrinsicTheamountthattheandotherwiseIntrinsicoption:C=max–X,0]Intrinsicputoption:P=max–S,0]Timetheoption(calleditsanditsintrinsicdueitstime73-123OptionsSTSTKKMax(ST–K,0)−Max(ST–K,0)STSTKKMax(K–T,0)−Max(K–T,0)74-123PropertiesCallOptionsCallOptionBoundsBounds00max(S0−PVK,0)0max(S0−PVK−PVivs,0)max(S0−PVK,0)0视红利情况而定PutOptionsPutOptionBoundsBoundsPV(K)PV(K)Kmax(PVK−0,0)max(PVK+PVivs−0,0)max(K−0,0)K视红利情况而定EuroCallPrice+PVK+PVivs=EuroPutPrice+SPut-Call75-123PropertiesWhatwillthelowerboundforthepriceaputoptiononanon-dividend-payingstockthestockpricethepriceUSD25,the6%per(annuallycompounded)?lowerbound(USD)25maxK−0,0=−22=2.64(1+0.06)5priceanon-dividend-payingstockandthepriceafour-monthcalloptiononthestockwithaprice4%per(annuallycompounded).Whatthepriceafour-monthoptiononthestockwithapriceAssumenoarbitrageopportunitiesexist.put-call:Put=Call+PV(K)-S30price(USD)isthusgivenby:2+−29=2.61104376-123CoveredCallandPut00STCallSTPutOptionCoveredCall=-C+SPrincipalNotes(PPN)Put=S+PAPPNasabondandanoptionwithathatanunderlyingasset,index,orbenchmark.Itguaranteesaminimumequaltheinvestment(theamount),theperformancetheunderlyingassets.77-123BullSpreadoutlookbullish00STSTBullPutSpreadBullCallSpread78-123outlookbearish00STSTBearCallSpreadSpreadBearPutSpreadAacombinationacallwithpricesKand1Kandabearwiththesametwoprices.2aalwaysK–K.2179-123ButterflySpread00STSTButterflySpreadButterflySpreadExpectslowCappedrisk80-123andACombinationoptiontradingthattakingapositionbothandputsonthesamestock.0ST0STAandaputSameneutralAandaputstraddle,butvolatility81-123ConclusionSimpleSpreadBullAshareandanoptionBotharecall,orbothareput2K2Kbutterfly3KCalendar2TCombination&Callandput82-123GapOptionsTheaoptionS−K,ifS≥K2T1TTheaputoptionK−S,ifS≤K21TTForwardStartOptionsAforwardstartoptionaputoroptionthatwillsomespecifiedtime.Itessentiallyaforwardonoption.83-123CompoundOptionsOptionsonoptionsAonaaputonaaonaput,andaputonaputIfoptionsthebetheonasingleoptionChooserOptionAfteraspecifiedperiodtime,thechoosewhethertheoptionaoraput.max(p)84-123BarrierOptionsanddependonthepriceacertainthetheoption.Aknock-outoptionexisttheunderlyingacertainwhileaknock-inoptiononlytheunderlyingasseta85-123BinaryOptions/DigitalOptionsCash-or-NothingsomeamountcashtheoptionAsset-or-NothingthetheunderlyingAcalloptionapositionasset-or-nothingandashortpositionacash-or-nothingAputoptionalongpositionacash-or-nothingputandashortpositionasset-or-nothingput.86-123LookbackOptionsonmaximumorminimumtheunderlyingassetWithfloatingstrikeandwithstrike.Callistre=MaxT−min,0Calldstre=Maxx−0Putstre=Max(Sx−T,0)Putdstre=Max(K−min,0)AsianOptionsonarithmetictheunderlyingassetpriceoptionandaveragestrikeoption.Callrice=Max−K,0Putrice=MaxK−avg,0=MAXS−S,0Calle=MaxS−S,0PTstreT87-123andSwapSwapExchangingvolatilityonanationalonand.SwapExchangingforOptionsReplicationforaportfoliooptionsoptions)thattheexoticoption.Shortingthispositionthe持续更新通知微：xuebajun888s88-1231:MBS12.Mortgages.Mortgage-BackedSecurities89-123MortgagesMonthlyamortizationthemonthlyandthemortgage(assumingnotForA30-yearU.S.mortgagethe6%withmonthlycompounding.IftheamountUSD300,000.USD1798.65monthfullyamortize(i.e.,USD300,00030years.90-123Mortgagesat300,000.00299,701.35299,401.20299,099.56298,796.40298,491.73…012345…1,500.001,498.511,497.011,495.501,493.98…298.65300.14301.65303.15304.67…1,754.351,763.121,771.941,780.801,789.7035635735835936044.307,105.575,342.443,570.501,789.700.0035.5326.7117.858.95InthefirstmonthTheonthemortgage.005xUSD300,000=USD1,500.00onthemortgageUSD1798.65-USD1,500.00=USD298.65091-123Mortgagestheoutstandingdiscountingremainingcashflow.thetheamount,theR(compoundedmonthly),andthemonthlyXX11−=AR/12+12TTyearsthethemortgage92-123MortgagesMortgageportfolios(mortgagepools)couponthethemortgagepoolandtheweightingeachmortgageproportionaltheoutstanding.similarlycalculatedastheaveragethenumbermonthswiththeeachmortgageproportionaltheoutstandingnnWAC=�wcWAM=�wLiiii1i=1nthenumbermortgagesthepool,cithecouponfortheithmortgage,Lithetheithmortgage.93-123MortgagesSMMOne-monthmortality(SMM)theoutstandingamonth.CPRAconstant(alsoconditionalannualizedSMM.=1−(1−1294-123Mortgage-BackedSecuritiesAgencyMortgage-BackedSecurities(MBSs)simplestmortgage-backedsecuritiessecurities(MPS),investorsapoolthesamerisksecuritiestradespecifiedpoolsandto-be-announced.95-123Mortgage-BackedSecuritiesAgencyMortgage-BackedSecurities(MBSs)DollarsellingTBAonemonthandbuyingasimilarTBAtheAsimilarsomeaButtwoimportant••Securitiespurchasedmonthbethosethefirstotherpartythetransactionsellthesamebutalsoasecuritywithalesstransactionsthelosingthewithspecifiedcoupon,theotherpartyone96-123Mortgage-BackedSecuritiesAgencyMortgage-BackedSecurities(MBSs)theA-B+C-DA:saletheforfirst(includingaccrued30daysmonth).B:secondmonthpool(includingC:ononesales.D:couponandforcapitalpoolthefirstmonth.97-123Mortgage-BackedSecuritiesForexampleSupposea4.5%poolwithaface$1millionwassolda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