一级章固定收益投资二衍生与另类

SS17–DerivativeAssignedSS17–DerivativeAssignedDerivativeMarketsandInstrumentsForwardMarketsandContractsFuturesMarketsandContractsOptionMarketsandContractsSwapMarketsandContractsRiskManagementApplicationsofOption12Defineaderivativeanddistinguishbetweenexchange-tradedandover-the-counterderivatives.AderivativeisDefineaderivativeanddistinguishbetweenexchange-tradedandover-the-counterderivatives.Aderivativeisafinancialinstrumentthatgivestheinvestorareturnbasedonperformanceofanunderlyingasset.••Exchange-tradedAretradedincentralizedlocationsandarestandardized,regulatedanddefaultriskfree.futuresandmany•Arecustomizedcontractscreatedbydealersandbyfinancialinstitutions.（forwards，swaps）Verylimitedtradinginsecondarymarketandexposedtocounterparty(default)risk.Someoptions,notablybond3Contrastforwardcommitmentsandcontingent•Aforwardcommitmentisalegallybindingpromisetoperformsomeactioninthefuture.Acontingentclaimisaclaim(toapayoff)thatdependsonaparticularevent.（未定债权，例子：期权）•4Defineforwardcontracts,futurescontracts,options(callsandputs),andswapsandcomparetheirbasiccharacteristics.Defineforwardcontracts,futurescontracts,options(callsandputs),andswapsandcomparetheirbasiccharacteristics.5Describepurposesofandcontroversiesrelatedtoderivative•Thecriticismofderivativesisthattheyare"toorisky,"especiallytoinvestorswithlimitedknowledgeofsometimescomplexinstruments.Becauseofthehighleverageinvolvedinderivativespayoffs,theyaresometimeslikenedtogambling.•Thebenefitsofderivativesmarketsarethatthey:Providepriceinformation.AllowrisktobemanagedandshiftedamongmarketReducetransactions6ExplainarbitrageandtheroleExplainarbitrageandtheroleitplaysindeterminingpricesandpromotingmarketefficiencyArbitragereferstoearningmorethantherisk-freewithnorisk,orearninganimmediategainwithnopossiblefutureliability..Arbitrageopportunitiesareshort-livedduetotheefficiencyofmarkets.Thecontinuingsearchforarbitrageopportunitieskeepspricesinline.lawofoneprice:twosecuritiesthathaveidenticalcashflowsinthefutureshouldhavethesameprice.IfaportfolioconsistingofAandBhasacertainpayoff,theportfolioshouldyieldtherisk-freerate.Ifthisisviolated,thenarbitrageoccurs.Anarbitrageurcouldborrowattherisk-freerate,buytheA+Bportfolio,andearnarbitrageprofitswhenthecertainpayoffoccurs7••••8BasicCharacteristicsofForwardTheseareagreementsbetweentwopartiesinwhichthebuyeragreestobuyfromthesellertheBasicCharacteristicsofForwardTheseareagreementsbetweentwopartiesinwhichthebuyeragreestobuyfromthesellertheunderlyingatafuturedateatapricewhichisspecifiedatthestart.Thebuyerhasalongforwardposition,iscalledthelong,andthesellerhasashortforwardposition,iscalledtheshort.Forwardmarketislargelyunregulated,andisExample:PartyAagreestobuya$1000facevalue,90dayTreasurybillfromPartyB30daysfromnowatapriceof$990.PartyAisthelongandBistheshort.If30daysfromnowT-billsaretradingat$992,theshortmustselltheT-billtothelongat$990.iftheT-billsaretradingat$988onthefuturedate,thelongmustpurchasetheT-billfromtheshortfor$990.Thereisdefaultrisk(counterpartyrisk).Thatistheriskthattheotherpartytothecontractwillnotperformatsettlement.DefaultriskexistswithallforwardAtanypointintime,includingthesettlementdate,onlyonepartytotheforwardcontractwillowemoney,meaningthatsideofthecontracthasanegativevalue.Theothersideofthecontracthasapositivevalueofanequal zero-sum9Theproceduresforsettlingaforwardcontractat•Deliverableforwardcontract-thelongwillpaythespecifiedpricetotheshort,whowilldelivertheunderlyingtothelong.Thisisthedeliveryprocess.•Cashsettlementisanalternativeandsimplerprocedure.Ontheexpiration(settlement)dateofthecontract,thelongreceivesapaymentifthepriceoftheassetisaboveforwardprice;theshortreceivesapaymentifthepriceoftheassetisbelowthecontractprice.TerminateForwardContractBefore•OnepartytothetransactionmaywishTerminateForwardContractBefore•Onepartytothetransactionmaywishtoterminatebeforeexpiration.Therearetwomethods:Enterintoanewforwardcontractwithanexpirationdateequaltothetimeremainingontheoriginalcontract,takingtheoppositepositionwithnewcounterparty.–exposecreditriskAnotheralternativeistoenterintothesecond(offsetting)contractwiththesamepartyastheoriginalcontract.Onepartywouldpaytheotherthepresentvalueoftheamountowedatexpiration.Thisavoidsallcreditrisk.ThisearlyterminationwillfixtheamountofthegainorlossatsettlementDistinguishbetweenadealerandanenduserofaforward•Anenduserismostancorporationthatwishestohedgerisk-thefirmhasariskandislookingforafinancialtransactiontoreduceit.Theenduser'sgoalistoreduceoreliminatethisrisk.•Dealersarespecialistsincertaincontractsormarkets.Atypicaldealerisalargeinternationalbankinginstitution,butnon-bankinginstitutionsarealsodealers.Dealerstypicallyengageintransactionswitheitherendusersorotherdealers.Theyearnabid-askspreadforcompensatingthecostsaswellasbearingdefaultriskandanyassetpriceriskfromunbalancedDescribethecharacteristicsofequityforwardcontractsandforwardcontractsonzero-couponandcouponbonds.•Describethecharacteristicsofequityforwardcontractsandforwardcontractsonzero-couponandcouponbonds.•Anequityforwardcontractmaybeonasinglestock,acustomizedportfolio,oranequityindex,andisusedtohedgetheriskofequitypricesatfuturedate.•Equityforwardcontractscanbewrittenonatotalreturnbasis(includingdividends),butaretypicallybasedsolelyonanindex•Indexforwardssettleincashbasedonthenotionalamountandthepercentagedifferencebetweentheindexvalueintheforwardcontractandtheactualindexlevelatsettlement.Example:Equityindexforward•Astheshortparty,theportfoliomanagermustpay2%*10million=$200000tothelong.ForwardContractsonZero-couponForwardcontractonT-billsForwardContractsonZero-couponForwardcontractonT-bills(zero-coupon)arequotedintermsofthediscountonzero-couponbonds•ForwardContractsonCouponCouponForwardcontractoncouponbondsarequotedintermsofyieldtomaturity，exclusiveofaccruedinterest.•Bondscarrydefaultrisk–Forwardsoncorporatebondmustcontainspecialprovisionstodealwiththepossibilityofthedefaultaswellaswithanycalls/convertibilityfeatures.ForwardscontractsmayalsobewrittenonportfoliosfixedincomesecuritiesoronbondDescribethecharacteristicsoftheEurodollartimedepositDescribethecharacteristicsoftheEurodollartimedepositmarket,anddefineLIBORandEuribor.EurodollardepositisthetermfordepositsinlargebanksoutsidetheUnitedStatesdenominatedinU.S.dollars.Thelendingrateondollar-denominatedloansbetweenbanksiscalledtheLondonInterbankOfferedRate(LIBOR).Itisquotedasanannualizedratebasedona360-dayLIBORisusedasareferencerateforfloatingrateU.S.dollar-denominatedloansworldwide.••••EuroequivalentofLIBOR.CompiledinFrankfurt.PublishedbyEuropeanCentralDescribeforwardrateagreements(FRAs)andcalculatethegain/lossonaFRAFRAisDescribeforwardrateagreements(FRAs)andcalculatethegain/lossonaFRAFRAisaforwardcontracttoborrow/lendmoneyatacertainrateatsomefuturedate.The"underlying"isaninterestrate.Cashsettlement,noactualloanismadeatthesettlementdate.ThelongpositioninanFRAisthepartywhowouldborrowtheforwardrateorcontractrateisthefixedratespecifiedinthecontract,theratethelongcouldborrow.ReferencerateisthefloatingrateonthesettlementPaymentsarebasedonthedifferencebetweentheforwardrateandthereferencerate(e.g.,LIBOR).Ifthefloatingrateatexpirationisabovetheforwardrate,longpositionwillreceivethePaymentatExpirationofanExample:ConsideranFRA•••Expires/settlesin30days.;Isbasedonanotionalprincipalamountof$1million.Isbasedon90-dayLIBOR;Specifiesaforwardrateof5%.Assumethattheactual90-dayLIBOR30-daysfromnow(atexpiration)is6percent.Computethecashsettlementpaymentatexpiration,andidentifywhichpartymakesthepayment.CalculateandinterpretthepayoffofaFRAandexplaineachofthecomponenttermsofthepayoffformula.ThegeneralformulaforthepaymenttoCalculateandinterpretthepayoffofaFRAandexplaineachofthecomponenttermsofthepayoffformula.Thegeneralformulaforthepaymenttothelongatsettlement•notionalprincipal(floating-forward)days3601+floatingdays360•Thenumeratoristhe"interestsavings"inpercent,andthedenominatoristhediscountfactor.Notethatifthefloatingrateunderlyingtheagreementturnsouttobebelowtheforwardratespecifiedinthecontract,thenumeratorintheformulaisnegativeandtheshortreceivesapaymentfromthelong.••60dayFRAon90dayLIBOR=2x•Ananalystdoesresearchaboutthedefinitionofforwardrateagreement(FRA).FRA3*12meansthematurityis:C3monthandisbasedona6-monthunderlyingrate.3monthandisbasedona9-monthunderlying9monthandisbasedona3-monthunderlyingDescribethecharacteristicsofcurrencyforwardcontractsDescribethecharacteristicsofcurrencyforwardcontractsCurrencyforwardcontractsspecifythatonepartywilldeliveracertainamountofonecurrencyatthesettlementdateinexchangeforacertainamountofanothercurrency.CurrencyforwardcontractscanbedeliverableorsettleinUndercashsettlement,thecashpaymentisbasedondifferencebetweentheexchangeratefixedinthecontractandthemarketexchangerateatthesettlementdate.••••AlargeU.S.firmhasaEuropeansubsidiary.Currencyforwardcontractsenablethefirmtolockintherateatwhichitwillselleurosandpurchasedollarsatthetimeinthefuture.CharacteristicsofCurrencyForwardDescribethecharacteristicsoffuturescontracts.Comparefuturescontractsandforwardcontracts.CanbeDescribethecharacteristicsoffuturescontracts.Comparefuturescontractsandforwardcontracts.CanbeeitherdeliverableorcashsettlementArepricedtohavezerovalueatthetimeaninvestorentersintothetradeonorganizedPrivatecontractsanddonothighlyCustomizedAsingleclearinghouseisthecounterpartytoallfuturecontracts-nocounterpartyriskContractswithoriginatingGovernmentNotDistinguishbetweenmargininthesecuritiesmarketsandmargininthefuturesmarkets•Margin,inDistinguishbetweenmargininthesecuritiesmarketsandmargininthefuturesmarkets•Margin,inbothequityandfuturesmarkets,allowsleverage,whichmagnifiesprofitsandlosses.IntheequityWithmargin,aloanisBorrowedfundsmustberepaidwithThereisaninitialmarginrequirement(typicallyaninvestorcanborrow50%ofinitialstockvalue),andamaintenancemarginrequirement(marketvalueofposition,lessamountborrowed,butbeatleastapercentage,typically25-30%).Ifthemarginaccountbalancegoesbelowthemaintenancemargin,fundsmustbedepositedtobringtheaccountbackuptothemaintenancemargin!Initialandmaintenancearesetby•Explaintheroleofinitialmargin,margin,variationmargin,andsettlementinfuturesInitialMarginrequiredonthefirstdayofthetransaction.Thisiswhatthefuturestraderputsupinitially-"goodfaith"money,performancebond.MaintenancemarginMarginrequirementonanyotherday,otherthantheinitialdayofthetransaction.Marginaccountbalancesaremonitored,andthemaintenancemarginistheminimumrequirementtobeleftintheaccount.VariationWhenbalancesfallbelowthemaintenancemargin,fundsmustbedepositedtobringthemarginaccountbalancebackuptotheinitialmarginrequirement.VariationmarginisthisadditionalSettlementTheofficialprice,whichisdesignatedbytheclearinghouse,fromwhichdailygains/losseswillbedeterminedandmarkedtomarket.Settlementpriceisanaverageofthepricesofthetradesduringthelastperiodoftrading,calledthe••••closingDescribepricelimitsandtheprocessofmarkingtoDescribepricelimitsandtheprocessofmarkingto•Manyfuturescontractshavepricelimits,whichareexchange-imposedlimitsonhowmuchthecontractpricecanchangefromthepreviousday’ssettlementprice.•Tradescannottakeplaceatpricesthatdifferfromthepreviousday’ssettlementpricesbymorethanthepricelimitandaresaidtobelimitdown(up)whenthenewequilibriumpriceisbelow(above)theminimum(maximum)priceforthe•Iftradescannottakeplacebecauseofalimitmove,eitherupordown,thepriceissaidtobelockedlimitsincenotradescantakeplaceandtradersare"locked"intotheirexistingDescribepricelimitsandtheprocessofmarkingto•Markingtomarketistheprocessofadjustingthemarginbalanceinafuturesaccounteachdayforthechangeinthevalueofthecontractassetsfromtheprevioustradingday,basedonthenewsettlementprice.当天无负债制度Calculateandinterpretthemarginbalance,giventhepreviousday'sbalanceandthechangeinthefuturesprice.•Example:ConsideralongpositionoffiveJulywheatcontracts,eachofwhichcovers5000bushels.Currentprice=$2/bushel,initialmarginrequirement=$150/contract,maintenancemarginrequirement=$100/contract.Assumetheinvestorislong5contracts,computeCalculateandinterpretthemarginbalance,giventhepreviousday'sbalanceandthechangeinthefuturesprice.•Example:ConsideralongpositionoffiveJulywheatcontracts,eachofwhichcovers5000bushels.Currentprice=$2/bushel,initialmarginrequirement=$150/contract,maintenancemarginrequirement=$100/contract.Assumetheinvestorislong5contracts,computethemarginbalance.Answer:apricechangeof$0.01perbushelchangesthecontractvalueby0.01*5000=$50,or$250for5contracts.initialmargin$750,maintenancemargin$••DescribehowafuturescontractcanbeterminatedatorpriortoAfuturespositionmaybeclosedoutviafourdifferentForexample,afuturescontractbuyerPhysicallydeliverthecontract,paythepre-specifiedpriceatdelivery,andreceivetheunderlyingassetatitscurrentvalue.cashMakeareversetrade,oroffsetting.Yourpositionhasbeenclosedout.Exchangeforphysicals-findatraderwithanoppositepositiontoyourownanddeliverthegoodsandsettleupbetweenyourselves,offtheflooroftheexchange.Youmustthencontacttheclearinghouseandtellthemwhathappened.••Deliveryoptionstotheshort:optionsonwhat,where,andwhentodeliver.620020010--230--DescribethecharacteristicsofTreasurybillsFutureAreDescribethecharacteristicsofTreasurybillsFutureArebasedona$1millionfacevalue90-dayT-billsettleinQuotation=100-r%，r=discountActualdeliveryprice=1,000,000*[1-AT-billpricequoteof98.52,computetheactualprice.P=1000000*[1-(90/360)*1.48%]=996300Ifyoutookalongpositionat98.52andthepricefellto98.50,youlossis$50percontract.OneBPchangepriceofDescribethecharacteristicsofEurodollarFutureArebasedon$1,000,000notionalprincipalof90-dayEurodollarsandsettleincash.Contractspaybasedon90dayLIBOR,andaremuchmoreactivelytradedthanT-billfuturescontracts.Quotation=100-annualizedLIBORinAquoteof97.6respondstoanannualizedLIBORof(100-97.6)=2.4%andaneffective90-dayyieldof2.4%/4=0.6%Minimumticksizeis1basispoint:T-billfutureshavelostimportanceinfavorofEurodollarfutures,whichrepresentamorefree-marketandmoreglobalmeasureofshort-terminterestrate34DescribethecharacteristicsofTreasuryBondFutureTreasurybondfutures•Underlying:U.S.DescribethecharacteristicsofTreasuryBondFutureTreasurybondfutures•Underlying:U.S.Treasurybondwithfacevalue$100000atleasta15yearmaturity.Areadeliverablecontract.Arequotedasapercentandfractionsof1%(measuredin1/32nds)offacevalue.Theshorthastheoptiontodeliveranyofseveralbondsthatwillsatisfythedeliverytermsofthecontract.Thisiscalledadeliveryoption,thefinalparticularTreasurybonddeliverediscalledthecheapest-to-deliverybond.Useconversionfactorstoadjustthecontractpriceforthebondthatisdelivered.Contractprice=futuresprice×conversionDescribethecharacteristicsofStockIndexFutureStockindexfuturesThemostpopularistheS&P500StockIndextradedontheChicagoMercantileExchange.SettlementincashandmultiplierisWithanindexlevelof1000,thevalueofeachcontractis$250000Eachpointinthefuturepricerepresentsagainorloss$250perAlongstockindexfuturespositiononS&P500StockIndexat1051wouldshowagainof$1750inthetrader’saccountiftheindexwere1058atthesettlement••dare($250*7=DescribethecharacteristicsofCurrencyFutureDescribethecharacteristicsofCurrencyFuture•Ananalystdoesresearchaboutdifferencebetweenforwardmarketandfuturemarket.Comparedwithcontractsintheforwardmarket,contractsinthefuturesmarketareleastlikelytobeappropriatelydescribedastransactionsthatare:Ccustomizedaccordingthecounterparts’basedonanagreementtobuyorsellanunderlyingassetatafuturedateatapriceagreedontoday.CallandputDistinguishbetweenEuropeanandAmericanEuropeanoption:canCallandputDistinguishbetweenEuropeanandAmericanEuropeanoption:canbeonlyexercisedonthedayofAmericanoption:canbeexercisedanytimeuptoandincludingthecontract’sexpirationday.Iftwooptionsareidenticalinallways,thevalueoftheAmericanoptionwillequalorexceedthevalueoftheEuropeanoption.Moneynessistherelationshipbetweenthepriceoftheunderlyingassetandtheoption'sexerciseprice:••••S>S<S=S=S<S>DefinetheconceptofmoneynessofanDefinetheconceptofmoneynessofanCompareexchange-tradedoptionsandover-the-counterExchange-tradedoptionsorlistedRegulated,Standardized,Widelytradedandguaranteedbyaclearinghouse.Generallyhaveshort-termexpirations.Over-the-counterSubjecttocounterpartyriskastheyarenotguaranteedbyaclearinghouse.IdentifythetypesofoptionsintermsofIdentifythetypesofoptionsintermsoftheunderlying•Financialoptionsincludeequityoptionsandotheroptionsbasedonstockindexes,Treasurybonds,interestrates,andcurrencies.Thestrikepriceforfinancialoptionscanbeintermsofyieldtomaturityonbonds,anindexlevel,oranexchangerateforforeigncurrencyoptions.LIBOR-basedinterestrateoptionshavepayoffsbasedonthedifferencebetweenLIBORatexpirationandthestrikerateintheBondoptionsaremoreoftenbasedonTreasurybondsbecauseoftheiractivetrading.Canbedeliverableorsettleincash.Thebuyerofacalloptiononabondwillgainifinterestratefallandbondpricesrise.Indexoptionsettleincash,nothingisdeliverable.Thepayoffonanc45••••DifferentTypesofDifferentTypesof•Optionsonfutures,sometimescalledfuturesDifferentTypesof•Optionsonfutures,sometimescalledfuturesoptions,givetheholdertherighttobuyorsellaspecifiedfuturescontractonorbeforeagivendateatagivenfuturesprice,thestrikeprice.Calloptionsonfuturesgivetheholdertherighttoenterintothelongsideofafuturesatagivenfuturesprice.putoptionsonfuturesgivetheholdertherighttoenterintotheshortsideofafuturesatagivenfuturesprice.•••Commodityoptionsgivetheholdertherighttoeitherbuyorsellafixedquantityofsomephysicalassetatafixed(strike)price.CompareinterestrateoptionswithforwardrateagreementsAninterestratecallhasapayoffequalto(thereferencerate-thestrikerate)timesthenotionalamountwhenthereferencerateexceedsthestrikerate.AputhasapayoffwhenthereferencerateisbelowthestrikeThelongcallreceivesapayoffwhenLIBORexceedsthestrikerateandreceivesnothingifLIBORisbelowstrikerate.TheshortputpositionmakespaymentifLIBORisbelowthestrikerate,andmakenopaymentswhenLIBORexceedsthestrikerate.Example:youboughta60-daycalloptionon90-dayLiborwithanotionalprincipleof$1millionandastrikerateof5%.Computethepaymentthatyouwillreceiveif90-dayLiboris6%atcontractexpiration,anddeterminewhenthepaymentwillbereceived.Longcallreceive(6%-Thisamountwillbepaidbythecallwriter90daysafterexpi8tion.InterestRateOptionsVSAlongpositioninanFRA=longinterestratecall+shortinterestputDefineInterestRateOptionsVSAlongpositioninanFRA=longinterestratecall+shortinterestputDefineinterestratecaps,floors,andInterestrateFixedForwardExerciseSettlementRightorsameforbothSettlementForwardexpirationbutatafuturedatecorrespondingtothetermofthereferencedateInterestRateCapsandCalculateandinterpretInterestRateCapsandCalculateandinterpretoptionpayoffsandexplainhowinterestrateoptionsdifferfromothertypesofoptions.Calculatingthepayoffforastockoption,orothertypeofoptionwithmonetary-basedexerciseprice,isAtexpiration,acallownerreceivesanyamountbywhichtheassetpriceexceedsthestrikeprice,andzerootherwise.Theholderofaputwillreceiveanyamountthattheassetpriceisbelowthestrikepriceatexpiration,andzerootherwise.Whilebondsarequotedintermsofyield-to-maturity,T-billsindiscountyield,indicesinindexpoints,andcurrenciesasanexchangerate,thesameprincipleapplies.Thatis,ineachcase,togetthepayoffperunitoftherelevantasset,weneedtotranslatetheassetvaluetoadollarvalueandthestrikeprice(orrate,oryield)toadollarstrikeprice.Wecanthenmultiplythispayofftimeshowevermanyunitsoftheassetarecoveredbytheoptionscontract.Forastockindexoption,wesawthatthesedollarvalueswereobtainedfrommultiplyingtheindexlevelandthestrikelevelbythemultiplierspecifiedinthecontract.Theresultingdollarpayoffsarepercontract.Thepayoffonoptionsonfuturesisthecashtheoptionholderreceiveswhenheexercisestheoptionandtheresultingfuturespositionismarkedtomar5k2et.•••••Thepayoffsoninterestrateoptionsare•ThepayoffsoninterestrateoptionsareDefineintrinsicvalueandtimevalue,andexplaintheir•Anoption’sintrinsicvalueistheamountbywhichtheoptionisin-the-money.Itistheamountthattheoptionownerwouldreceiveiftheoptionwereexercised.Anoptionhaszerointrinsicvalueifitisatthemoneyoroutofthemoney,regardlessofwhetheritisacalloraputoption.•Anoption’stimevalueofanoptionistheamountbywhichtheoptionpremiumexceedstheintrinsicvalueandissometimescalledthespeculativevalueoftheoption.•Foraparticularoption,thesumofthesevaluesequalstheoption'stotalvalue:Optionvalue=Intrinsicvalue+TimeIntrinsicCallOptionPayoffLong0StockpriceIntrinsicCallOptionPayoffLong0StockpriceX=PutOptionPayoffLongPutOptionPayoffLongAnanalystdoesresearchaboutmoneynessofstockoptions.Withrespecttostockoptions,thepotentialforaninfinitelossexistsforaninvestorwho:sellsaputbuyaputsellsacall•Aninvestorpaid$5foraputoptionthatwasin-the-money$3.Ifthepriceoftheunderlyingwas$58atthetimetheinvestorpurchasedthe•Aninvestorpaid$5foraputoptionthatwasin-the-money$3.Ifthepriceoftheunderlyingwas$58atthetimetheinvestorpurchasedtheputoption,theexercisepriceofthatputoptionwasclosestto:A.B.C.DeterminetheminimumandmaximumvaluesofEuropeanoptionsandAmericanoptions.CalculateandinterpretthelowestpricesofEuropeanandAmericancallsandputsbasedontherulesforminimumvaluesandlowerbounds.DerivethelowerboundofEuropeanPFA:alongat-the-moneycallwithCalculateandinterpretthelowestpricesofEuropeanandAmericancallsandputsbasedontherulesforminimumvaluesandlowerbounds.DerivethelowerboundofEuropeanPFA:alongat-the-moneycallwithstrikeX,expiringat+alongdiscountbondpricedatrthatpayXatTPFB:astockAttimeT:PFAalways>=PFSo…Attime0:PFAmustalso>=PFSo…c0+X/(1+r)T>=→c0>=S0-→c>=S-X/(1+r)T-ttTimeTimePFXPFLowerUpperEuropeanct>=Max[0,St-X/(1+RFR)T-AmericanCt>=Max[0,St-X/(1+RFR)T-Europeanpt>=Max[0,X/(1+RFR)T-t-X/(1+RFR)(T-AmericanPt>=Max[0,X-XLowerboundofAmerican•AnAmericancallisworthatleastasmuchasaEuropeancallLowerboundofAmerican•AnAmericancallisworthatleastasmuchasaEuropeancalltoclaimthatthelowerboundonanAmericancallisatleastasmuchasthelowerboundonaEuropeancall.CalculatetheLowest•Ananalystdoesresearchaboutoptionvalue.•Ananalystdoesresearchaboutoptionvalue.Whichofthefollowingstatementsismostaccurate?Priortoexpiration,themaximumvalueofanAmericancallisexcisecurrentpriceoftheunderlying.presentvalueoftheexerciseprice.Explainhowoptionpricesareaffectedbytheexercisepriceandthetimetoexpiration.•Callpricesareinverselyrelatedtoexerciseprices.IfX1>X2,thenC1<C2Putpricesaredirectlyrelatedtoexerciseprices.IfX1>X2,thenP1>P2•212.Ananalystdoesresearchaboutoptionvalue.Ingeneral,withrespecttotwocalloptionsonthesameunderlying,istheoptionwithhighervaluelikelytohavea: longertime212.Ananalystdoesresearchaboutoptionvalue.Ingeneral,withrespecttotwocalloptionsonthesameunderlying,istheoptionwithhighervaluelikelytohavea: longertimetohigherexerciseprice?CExplainput-callparityforEuropeanoptions,andexplainhowput-callparityisrelatedtoarbitrageandtheconstructionofsyntheticoptions.Afiduciarycallisacombinationofapure-discount,risklessbondthatpaysXatmaturityandacallwithexercisepriceX.Aprotectiveputisashareofstocktogetherwithaputoptiononthestock.put-callparity:c0+X/(1+r)T=S0+TimeTimeST-ProtectiveX-STPut-callParityforEuropean•EquivalenciesforeachofthePut-callParityforEuropean•Equivalenciesforeachoftheindividualsecuritiesintheput-callparityrelationshipcanbeexpressedas:•••••S=c–p+X/(1+p=c–S+X/(1+RFR)c=S+p–X/(1+TTTX/(1+ =S+p–TThesinglesecuritiesontheleft-handsideoftheequationsallhaveexactlythesamepayoffsastheportfoliosontheright-handside.Theportfoliosontheright-handsidearethe“synthetic”equivalentsofthesecuritiesontheleft.NotethattheoptionsmustbeEuropean-styleandtheputsandcallsmusthavethesameexercisepricefortheserelationstohold.Put-callParityforEuropeanExplainhowcashflowsontheunderlyingassetaffectput-callExplainhowcashflowsontheunderlyingassetaffectput-callparityandthelowerboundsofoptionprices.•Cashflowsontheunderlyingassetcanaffectput-callparity,andthusthelowerboundsofoptionpricesbydecreasingtheunderlyingpricebythepresentvalueofthecashflowsovertheoption'slife.•RestatedlowerboundsforEuropeanoptionsattimet=0:c0≥Max[0,S0–PVCF–X/(1+RFR)T]p0≥Max[0,X/(1+RFR)T–(S0–•Restatedput-call(S0–PVCF)=C–P+X/(1+RFR)T,andC+X/(1+RFR)T=(S0–PVCF)+PDeterminethedirectionaleffectofaninterestratechangeorvolatilitychangeonanoption'sprice.•Agreaterinterestraisesthepriceofacalllowersthepriceofaput•Increasedvolatilityoftheunderlyingassetorinterestrateincreasesbothputvaluesandcallvalues.•Ananalystdoesresearchaboutimpact•Ananalystdoesresearchaboutimpacttooptionduetointerestrateandvolatilityoftheunderlying.Whichofthefollowingstatementsbestdescribestheeffectofthelevelofinterestratesandvolatilityoftheunderlyingonthepriceofoptions?Allelsebeingequal,pricesfor:Putoptionsarepositivelyrelatedtothelevelofinterest Calloptionsarepositivelyrelatedtothelevelofinterestrates PutoptionsarenegativelyrelatedtothevolatilityoftheunderlyingCharacteristicsofSwapAswapisanCharacterist