CFA二级-集训营直播-衍生-习题.docx

(906I0Z)尹喉皿PricingandvaluationofforwardcontractCarryarbitragemodel6R39 Pricing and Valuation of Forward Commitments Pricing and Valuation of FRA Pricing and Valuation of fixed income futuresPricingandValuationofSwap*DerivativesR40ValuationofContingentClaimsBinomialOptionValuationModel3)Black-Scholes-Merton(BSM)model®OptionGreeksDerivativesApplicationR41DerivativesStrategiesoptionstrategies®equityforwardcontractsequityindexforwardcontractsPricingandVdlUdtiorlofforwardContQCtcurrencyforwardcontractsfixedincomeforwardcontractsCarry arbitrage modelCash-and-carryArbitrage:F0>S0(1÷r)TReverseCash-and-CarryArbhrage:FO(T)<S0(1÷)aT Pricing and Valuation of FRADefinationPricing and Valuation of fixed income futures Interest Rate Swap contractsPricing and Valuation of Swap Currency swap contractsEquity swap contractsR39PricingandValuationofForwardCommitmentsOne-period binomial model Binomial Option Valuation ModelHedge ratioTwo-period binomial modelR40 Valuation ofContingent ClaimsBlack-Scholes-Merton (BSM) modelBinomialinterestratetreeAssumption/FormuIasZInterpretationBSMmodelsforoptionsonfutures,interestrateoptionSwaptionOptk>nGreeksOptionGreeksDeltahedgeThefollowinginformationrelatestoQuestions1-7DonaldTroubadourisaderivativestraderforSouthernShoresInvestments.Thefirmseeksarbitrageopportunitiesintheforwardandfuturesmarketsusingthecarryarbitragemodel.Exhibit1.CurrentDataforFuturesandUnderlyingBondFuturesContractUnderlyingBondQuotedfuturesprice125.00Quotedbondprice112.00Conversionfactor0.90Accruedinterestsincelastcouponpayment0.08TimeremainingtocontractexpirationAccruedinterestoverlifeoffuturescontractThreemonths0.00Accruedinterestatfuturescontractexpiration0.20Troubadouridentifiesanarbitrageopportunityrelatingtoafixed-incomefuturescontractanditsunderlyingbond.CurrentdataonthefuturescontractandunderlyingbondarepresentedinExhibit1.Thecurrentannualcompoundedrisk-freerateis0.30%.Troubadournextgathersinformationonthreeexistingpositions.Position1(Nikkei225FuturesContract):TroubadourholdsalongpositioninaNikkei225futurescontractthathasaremainingmaturityofthreemonths.ThecontinuouslycompoundeddividendyieldontheNikkei225StockIndexis1.1%,andthecurrentstockindexlevelis16,080.Thecontinuouslycompoundedannualinterestrateis0.2996%.Position2(Euro/JGBForwardContract):Onemonthago,Troubadourpurchasedeuro/yenforwardcontractswiththreemonthstoexpirationataquotedpriceof100.20(quotedasapercentageofpar).Thecontractnotionalamountis¥100,000,000.Thecurrentforwardpriceis100.05.,.Case1Position3(JPY/USDCurrencyForwardContract):Troubadourholdsashortpositioninayen/USdollarforwardcontractwithanotionalvalueof$1,000,000.Atcontractinitiation,theforwardratewas¥112.10per$1.Theforwardcontractexpiresinthreemonths.Thecurrentspotexchangerateis¥112.00per$1,andtheannuallycompoundedrisk-freeratesare-0.20%fortheyenand0.30%fortheUSdollar.Thecurrentquotedpriceoftheforwardcontractisequaltotheno-arbitrageprice.TroubadournextconsidersanequityforwardcontractforTexasSteel,Inc.(TSI).InformationregardingTSIcommonsharesandaTSIequityforwardcontractispresentedinExhibit2.Exhibit2SelectedInformationforTSIThepricepershareofTSscommonsharesis$250.Theforwardpricepershareforanine-monthTSIequityforwardcontractis$250.562289.Assumeannualcompounding.TroubadourtakesashortpositionintheTSIequityforwardcontract.Hissupervisorasks,Underwhichscenariowouldourpositionexperiencealoss?"Threemonthsaftercontractinitiation,TroubadourgathersinformationonTSIandtherisk-freerate,whichispresentedinExhibit3.Exhibit3.SelectedDataonTSlandtheRisk-FreeRateThepricepershareofTSscommonsharesis$245.Therisk-freerateis0.325%(quotedonanannualcompoundingbasis).TSlrecentlyannounceditsregularsemiannualdividendof$1.50persharethatwillbepaidexactlythreemonthsbeforecontractexpiration.ThemarketpriceoftheTSIequityforwardcontractisequaltotheno-arbitrageforwardprice.三.0d.0qsdv-O二sosooSI0SCOQSU-InJnJPUoqUoJlJoJd2olPu-PUnOdLuo。WnUUPMUlEnSSEPUP-IIqIqXXUopgspCQ-2.Thecurrentno-arbitragefuturespriceoftheNikkei225futurescontract(Position1)isclosestto:A.15,951.81.B.16,047.86.C.16,112.21.3.ThevalueofPosition2isclosestto:A.-¥149,925.B.-¥150,000.C.-¥150,075.4.ThevalueofPosition3isclosestto:A.-¥40,020.B.¥139,913.C.¥239,963.心段.qjphJP。OS。AUJUoPuSEq-U.sAm。UoPgSEq三.9qEUEAP-OU<ISHO)AJ-UlTUOddO°MPJ=qpUPIPP三J三OOOHZJ-q-qxwUomc-EnbgUS-。-WC1。EJlU0。PJuoJg三g?Jd-gw=OSEUUPEUIpnbu=PC巨8l三wcUP-3?=E/Oyd2PqSSjSl三sE<-Sl-ObcooPJBMJoJ-HMU-PJPMg-IUO=SUnbSeJoS【AJgdns-ortOHOJUSUOdSO-IWJdO-IddPJSoUJoqH96I99SUI9gIssPQ6寸S9sv-O二s<DsooSIU.2J.21C二QPJlU0。JgUPSqlUouIgJ三pi=uosoHl.三uo三sod§SCJnoPPqnoJl三EA2EqSJgdUWobu一PImodIU0。WnUUEcsrtPUEEPUENs-qqxwUoPUSEgcCase2ThefollowinginformationrelatestoQuestions8-16TridentAdvisoryGroupmanagesassetsforhigh-net-worthindividualsandfamilytrusts.AliceLee,chiefinvestmentofficer,ismeetingwithaclient,NoahSolomon,todiscussriskmanagementstrategiesforhisportfolio.SolomonisconcernedaboutrecentvolatilityandhasaskedLeetoexplainoptionsvaluationandtheuseofoptionsinriskmanagement.OptionsonStock1.eebegins:WeusetheBlack-Scholes-Merton(BSM)modelforoptionvaluation.TofullyunderstandtheBSMmodelvaluation,oneneedstounderstandtheassumptionsofthemodel.Theseassumptionsincludenormallydistributedstockreturns,constantvolatilityofreturnontheunderlying,constantinterestrates,andcontinuousprices.”LeeusestheBSMmodeltopriceTCB,whichisoneofSolomon,sholdings.Exhibit1providesthecurrentstockprice(三),exerciseprice(X),risk-freeinterestrate(r),volatility(),andtimetoexpiration(T)inyearsaswellasselectedoutputsfromtheBSMmodel.TCBdoesnotpayadividend.Exhibit1.BSMModelforEuropeanOptionsonTCBBSMInputsSXrr$57.03550.22%32%0.25BSMOutputsBSMBSMdijV(<)<2N(d*CallPricePutPrice0.31000.62170.15000.5596$4,695$2,634OptionsonFuturesTheBlackmodelvaluationandselectedoutputsforoptionsonanotherofSolomon,sholdings,theGPX500Index(GPX),areshowninExhibit2.ThespotindexlevelfortheGPXis187.95,andtheindexisassumedtopayacontinuousdividendatarateof2.2%()overthelifeoftheoptionsbeingvalued,whichexpirein0.36years.AfuturescontractontheGPXalsoexpiringin0.36yearsiscurrentlypricedat186.73.Exhibit2.BlackModelforEuropeanOptionsontheGPXIndexBlackModelInputsGPXIndexXrYieldBlackModelInputsGPXIndexXrr6Yield187.951800.39%24%0.362.2%BlaCk'IodelCallValueBlackModelPutValueMarketCallPriceMarketPutPriceS14.2089$7.4890S14.26$7.20OptionGreeksDelta(call)Delta(put)Gamma(callorput)Thcta(call)dailyRho(call)per%VCgaper%(callorput)0.6232-0.36890.0139-0.03270.37050.4231AfterreviewingExhibit2,SolomonasksLeewhichoptionGreekletterbestdescribesthechangesinanoption,svalueastimetoexpirationdeclines.SolomonobservesthatthemarketpriceoftheputoptioninExhibit2is$7.20.LeerespondsthatsheusedthehistoricalvolatilityoftheGPXof24%asaninputtotheBSMmodel,andsheexplainstheimplicationsfortheimpliedvolatilityfortheGPX.OptionsonInterestRatesSolomonforecaststhethree-monthLiborwillexceed0.85%insixmonthsandisconsideringusingoptionstoreducetheriskofrisingrates.HeasksLeetovalueaninterestratecallwithastrikepriceof0.85%.Thecurrentthree-monthLiboris0.60%,andanFRAforathree-monthLiborloanbeginninginsixmonthsiscurrently0.75%.HedgingStrategyfortheEquityIndexSolomon,sportfoliocurrentlyholds10,000sharesofanexchange-tradedfund(ETF)thattrackstheGPX.Heisworriedtheindexwilldecline.HeremarkstoLee,tYouhavetoldmehowtheBSMmodelcanprovideusefulinformationforreducingtheriskofmyGPXposition."LeesuggestsadeltahedgeasastrategytoprotectagainstsmallmovesintheGPXIndex.1.eealsoindicatesthatalongpositioninputscouldbeusedtohedgelargermovesintheGPX.Shenotesthatalthoughhedgingwitheitherputsorcallscanresultinadelta-neutralposition,theywouldneedtoconsidertheresultinggamma.0>5oeInqeobUJm2XOOJSUu2qSIPsg三louInqSgSJdSnonUPUoooSnonUHUo°OUJnqSUMscv-OjPJE0A(nJqEM3EJn8ES二UpoluSS0。JoSUopdUJnSSPOqlInoqEluIU-EISSe*39.BasedonExhibit1andtheBSMvaluationapproach,theinitialportfoliorequiredtoreplicatethelongcalloptionpayoffis:A.long0.3100sharesofTCBstockandshort0.5596sharesofazero-couponbond.B.long0.6217sharesofTCBstockandshort0.1500sharesofazero-couponbond.C.long0.6217sharesofTCBstockandshort0.5596sharesofazero-couponbond.10.TodeterminethelongputoptionvalueonTCBstockinExhibit1,thecorrectBSMvaluationapproachistocompute:A.0.4404timesthepresentvalueoftheexercisepriceminus0.6217timesthepriceofTCBstock,B.0.4404timesthepresentvalueoftheexercisepriceminus0.3783timesthepriceofTCBstock.C.0.5596timesthepresentvalueoftheexercisepriceminus0.6217timesthepriceofTCBstock.11.Whatarethecorrectspotvalue(三)andtherisk-freerate(r)thatLeeshoulduseasinputsfortheBlackmodel?A.186.73and0.39%,respectivelyB,186,73and2,20%trespectivelyC.187.95and2.20%,respectively12.WhichofthefollowingisthecorrectanswertoSolomon'squestionregardingtheoptionGreekletter?A.VegaB.ThetaC.Gamma13.BasedonSolomon,sobservationaboutthemodelpriceandmarketpricefortheputoptioninExhibit2,theimpliedvolatilityfortheGPXismostlikely:A.lessthanthehistoricalvolatility.B.equaltothehistoricalvolatility.C.greaterthanthehistoricalvolatility.14.ThevaluationinputsusedbyLeetopriceacallreflectingSolomon,sinterestrateviewsshouldincludeanunderlyingFRArateof:A.0.60%withsixmonthstoexpiration.B.0.75%withninemonthstoexpiration.C.0.75%withsixmonthstoexpiration.15.ThestrategysuggestedbyLeeforhedgingsmallmovesinSolomon,sETFpositionwouldmostlikelyinvolve:A.sellingputoptions.B.sellingcalloptions.C.buyingcalloptions.WJ(uffl>¾c.<-SIIPiPH0O=OJ仁OdPU二一nsgj-g*-二SoUJp_noMUo=-Sod工HSeUolUoOSJOJ-rtbUapuqPUSPqJnd1.-