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DerivativesLecture#51DerivativesDerivativesDefinition:Aderivativesecurityisasecuritywhosemarketvalueisdeterminedbythevalueofanother,underlyingsecurityFunctionshedgingspeculationRisksinabilitytounderstandinabilitytoformaperfecthedgecost2DerivativesDerivativeInstrumentsMarketsTradedorlistedmarketsOTCHedgingInstrumentsInsuranceInstruments3DerivativesHedgingInstrumentsForwardcontractsAcontractagreedupontotodaytodeliveraspecifiedgoodataspecifiedpriceataspecifiedfuturedateFuturescontractsAstandardized,exchange-tradedforwardcontractForwardRateAgreementsTakeaviewastofutureinterestratesSwapsAnexchangeofinterestand/orcurrencyflows

4DerivativesInsuranceContractsOptionContractsTheright,butnottheobligation,toeitherbuy(calloption)orsell(putoption)somethingataspecifiedpriceforaspecifiedperiodoftime.Floors,capsandcollarsMethodsofchangingtheinterestrateriskofafloatingratedebtobligationSwaptionsAnoptiontoenterintoaswapataspecifiedfuturedate5DerivativesForwardContractsMarketPriceDeliveryPrice+-0PayoffDiagram:LongtheForwardYoutakedeliverywhenlongtheforward.Thelongforwardpositionwillbenefitwhenmarketpricesriseafterthecontractisinitiated.6DerivativesForwardContractsMarketPriceDeliveryPrice+-0PayoffDiagram:ShorttheForwardYoumakedeliverywhenshorttheforward.Theshortforwardpositionwillbenefitwhenmarketpricesfallafterthecontractisinitiated.7DerivativesForwardMarkets&

Interest

RatesThemostliquidforwardmarketisthe“when-issued”TreasuryBillmarket.Dealersandinvestorsbuyandselltheas-yet-unissuedTreasuryBillfordeliveryimmediatelyaftertheyareissuedatauction.Theactivityinthe“when-issued”marketisagoodindicatorofwherethemarketbelievesratesareheaded8DerivativesHedgingInterestRateswithForwardContractsSupposeyouareholding$1,000,000insixyear,8%couponEurobondscurrentlytradingatpar.Youbelievethatinterestrateswillsoonriseby2%.Howdoyouhedgetheportfolio?Step#1:Calculatethebond’sdurationDuration=4.99271Step#2:PredictcapitallossP=(-D)(P)(R/1+R)=-$92,457Step#3:Adjustforconvexity(orcalculateactualpriceatnewmarketinterestrateof10%)Price=$912,894.79Actuallossthusequalto$1,000,000-912,894.79=$87,105.219DerivativesHedgingInterestRateswithForwardContractsStep#4:HedgeSellthebondforwardforsaleinsixmonthsatapriceof$100per$100offacevalue.Ifinterestratesriseaspredicted,purchasethebondinthemarketfor$912,894.79anddeliverundertheforwardcontract.Collect$1,000,000.Profitontheforwardexactlyoffsetsthelossonthebondportfolio.Ifratesfallinsteadofrise,youwillincuraloss,asyouwillhavetodeliverthebondatapricebelowitsmarketprice.10DerivativesComparingFutures&ForwardsForward FutureStandardizedNoYesExchange-tradedNoYesMarked-to-marketNoYesProfits&lossessettleddailyNoYesMarginrequiredNoYesExistenceofclearinghouseNoYes11DerivativesForwardRateAgreementsAssumethat,asabankmanager,youarefacingthefollowingsituation:Sixmonthinterestratesare10.5%.Threemonthinterestratesare10%.Whatthreemonthinterestrate,threemonthsfromtoday,wouldmakeusindifferentbetweeninvestinginonesixmonthinstrumentortwo,threemonthinstruments?Howcouldthebankprofitfromthisinformation?12DerivativesForwardRateAgreements10.5%10%X%ThreemonthsThreemonthsSixMonths13DerivativesForwardRateAgreementsTosolvetheproblem,wemustsolvethefollowingequationfortheforwardinterestrate,rfwd/fwd:14DerivativesForwardRateAgreementsWhere:D-numberofdaysintheperiodB-AnnualbasisrLong-ThespotsixmonthinterestraterShort-Thespotthreemonthinterestraterfwd/fwd-Thethreemonthforwardinterestrate15DerivativesForwardRateAgreementsSolvingtheproblem,weobtainthefollowingsolution:16DerivativesForwardRateAgreementsAtayieldof10.7342%onthreemonthmoneythreemonthsfromtoday,youwouldbeindifferentbetweeninvestinginonesixmonthinstrumentortwo,threemonthinstruments.Howcouldthebankmanagerprofitfromthisinformation?Ifthebankisabletoobtaintwo,threemonthdepositsatarateof10%andthenlendthemoneyat10.5%,thebankisassuredofmakingaprofitbasedonthemismatchinterm.17DerivativesForwardRateAgreementsBankschangetheirGAPwhentheyborrowandlendwithdifferentmaturities.NegativeGAPoccurswhenthebankborrowsshorttermandlendslongterm.Theriskisthatshortinterestrateswillrisebeforethelongassetmatures.Howwouldwecalculatetheprofitthebankwouldmakeifitcouldborrow$100,000,000at10%fortwo,threemonthperiodsandinvestthefundsat10.5%forsixmonths?18DerivativesForwardRateAgreementsTosolvetheproblem,usethefollowingformula:19DerivativesForwardRateAgreementsProblemswithusingforward/forwardsCreditrisk-thebankincurscreditriskonthelendingtransactionCapitalcharges-thebankmustholdadditionalcapitalagainstitslargerbalancesheetLinesofcredit-thebankisusingupitscreditcapacitywiththeborrowingtransactionTransactioncosts-thebankincurscostsinbothborrowing&lendingPolicyconflicts-thebankistryingtoadjustitsinterestrateriskpositionanditsborrowingandlendingactivitieswithoneinstrument-theBalanceSheet20DerivativesForwardRateAgreementsThesolutiontotheproblemistouseaForwardRateAgreementAforwardrateagreement(FRA)isidenticaltoaforwardcontractindeposits,exceptnodepositisevermade.FRAsallowbanks&corporatesto“bet”onfutureinterestrateswithoutaffectingthesizeoftheirbalancesheets.Ineffect,theFRAallowsthebankto““unbundle”thecreditriskcomponentfromtheinterestrateriskcomponent.21DerivativesForwardRateAgreementsSomedefinitions:FRA-afinancialcontractwhichcommitsonepartytocompensatetheotherpartyiftheinterestratewhichactuallyprevailsinthemarketplaceatsomefuturedatediffersfromtherateagreeduponbetweenthemtoday.Counterparties-referredtoasbuyersorsellersFRABuyer-profitsifinterestratesriseFRASeller-profitsifinterestratesfallInterestRatesContractReferenceRate-theinterestratewhichisfixedatthestartoftheFRAcontractSettlementRate-themarketrateatthestartofthenotionaldeposit22DerivativesForwardRateAgreementsMoredefinitions:Netcompensationamount-theamountofmoneyrequiredtosettletheFRA.EqualtothedifferencebetweentheContractReferenceRateandtheSettlementRatemultipliedbytheNotionalPrincipalAmount,scaledbythetermoftheFRA.ContractPeriod-thetermofthenotionaldepositonwhichtheFRAisbased.FRAcontractsareusuallydescribedintermsoftheperiodstoSettlementandMaturity.AFRAona6monthnotionaldepositcommencinginthreemonthswouldbedescribedasa3’’s,9’’sor3against9andisusuallywrittenas3v9.23DerivativesForwardRateAgreementsTodayStartDateofNotionalDepositMaturitydateofNotionalDeposit03Months6MonthsExampleofa3by6FRAThenotionaldepositstarts3monthsfromtodayandmaturessixmonthsfromtoday.Sincenodepositisactuallymade,thepartywhichhas“lostthebet””willmakeapaymenttotheotherpartycalculatedasthedifferencebetweentherateagreedtointheFRAandthecurrentmarketratefortheagreedmaturityofdepositatthetimethenotionaldepositismade.PricingisusuallydoneagainsttheBArate(inCanada)orLIBOR.24DerivativesForwardRateAgreementsPotentialproblemswithFRAs:Insomejurisdictions,thecontractmaybeconstruedasagamblingcontract,creatingenforceabilityproblems.Thebestdefenseisgooddocumentation.DuetothetremendousleverageofFRAscomparedtofwd/fwds,thesizeofthebetsthatcanbeplaced,relativetothebank’’sBalanceSheet,aremuchlarger.TheFRApayoffoccursatthestart,nottheend,ofthenotionaldepositperiod.Thiscanleadtocashflowproblems.25DerivativesOptionsMarketsOptionsarederivativesecuritieswhichallowaninvestorto......eitherlayoffrisk...ortoassumeadditionalrisk(toearnahigherreturn).Optionsalsoallowaninvestortoprofitfrom......eitheranincreaseordecreaseinthepriceofasecurity...ortoprofitwhenthepricedoesnotmoveatall.26DerivativesOptionsStraddleStripStrapPutsCalls1221OptionstobuyOptionstosellSpread27DerivativesOptionsDefinitionsCallOption-AcalloptiongivesthebuyertherightbutnottheobligationtobuyataspecifiedpriceforaspecifiedperiodoftimePutOption-AputoptiongivesthebuyertherightbutnottheobligationtosellataspecifiedpriceforaspecifiedperiodoftimeExercisePrice(StrikePrice)-Thepricepaid(orreceived)forthestockuponexercise.Expiration(Termination)Date-Thelastdateonwhichtheoptioncanbeexercised.AmericanOption-Isabletobeexercisedatanypointduringtheoption’slife.EuropeanOption-IsidenticaltoanAmericanOptionexcepttheoptioncanonlybeexercisedonit’’sexpirydate.28DerivativesHistoryofOptionTradingCalloptiontradingintheUS.beganinApril,1973withthecreationoftheChicagoBoardOptionsExchangePutoptiontradingwasintroducedin1977Canadiancalls&putsstartedtradingapproximatelyoneyearafterthoseintheUS29DerivativesVariablesAffectingOptionPricesFactorswhichwillaffectthepriceoftheoptioninclude:TimeperiodbeforeexpiryVariabilityofstockpricesRiskfreeinterestrateExercisepricevis-a-visstockprice30DerivativesProfitGraph-CallBuyerProfitLoss0MarketPriceofCommonStockZExercisePriceNote:Maxlossisthepremiumbutprofitsareunlimited31DerivativesProfitGraph-CallWriterProfitLoss0MarketPriceofCommonStockZNote:MaxprofitisthepremiumbutlossesareunlimitedExercisePrice32DerivativesCommonStockasaCallOptionProfitLoss0MarketPriceofthefirm’sassetsConclusion:commonstockofallleveraged,limitedliabilityfirmscanberegardedasacalloptiononthefirm’’sassetswithanexercisepriceequaltothefaceamountofthefirm’sdebt.ExercisePriceEqualtoFaceAmountofDebt45%line33DerivativesSomemoredefinitionsOutofmoneyAtthemarketInthemoneyDeepinthemoneyMaximumValueLineMinimumValueLine34DerivativesSomemoredefinitions...8MaximumValueLineMonthsBeforeExpiryExercisePrice42OutoftheMoneyAttheMoneyIntheMoneyDeepintheMoneyMinimumValueLine35DerivativesProfitGraph-PutBuyerExercisePriceZMarketPrice0ProfitLossNote:MaxprofitachievedifpriceofC.S.fallstozero.Maximumlossisvalueofpremium.36DerivativesProfitGraph-PutWriterExercisePriceZMarketPrice0ProfitLossNote:MaximumlossissustainedifC.S.fallstozero.Maximumprofitisvalueofpremium.37DerivativesFactorsWhichDeterminePutPremiumsTimebeforeexpirationPricevolatilityoftheoptionedsecurityRiskfreeinterestrateExerciseprice38DerivativesExercisePriceMarketPriceofOptionedSecurity0ProfitLossStraddles(1Put+1Call)Premiumpaid=Premiumfor1Call+1Put39DerivativesExercisePriceMarketPriceofOptionedSecurity0ProfitLossStrips(2Puts+1Call)Premiumpaid=Premiumfor2Puts+1Call40DerivativesExercisePriceMarketPriceofOptionedSecurity0ProfitLossStraps(2Calls+1Put)41DerivativesExercisePriceMarketPriceofOptionedSecurity0ProfitLossSpread(1Call+1Put)PutCallMarketPriceWhenOptionWrittenCBA42DerivativesWritingOptions:

CoveredorNakedAnoptionwriterissaidtohavewrittenacoveredoptionwhentheyalsoowntheunderlyingoptionedsecurity.Bywritingcoveredoptions,theoptionwriterreducestheriskofunfavorablepricemovements.43DerivativesExercisePriceMarketPriceofOptionedSecurity0ProfitLossProfitGraphCoveredCallWriterAbovetheexerciseprice,profit=premium.Belowtheexercisedprice,thelossonholdingthecommonlongispartiallyoffsetbythecallpremium.Premium44DerivativesCaps,FloorsandCollarsCapsareO-T-CinterestrateoptionsofferedbyfinancialinstitutionstoprovideinsuranceagainstunexpectedincreasesininterestratesabovesomepredeterminedlevelThecapensuresthattheratepaidonafloatingrateliabilityistheloweroftheprevailingmarketrateorthecaprate

Example:Acorporatehasa$10milliondollarloanonwhichitpaysthreemonthLIBOR.Abankhasprovidedaninterestratecapof10%perannum.Attheendofeachquarter,thefinancialinstitutionsellingthecapwillpaytotheborrower:

0.25x10,000,000xmax.(R-0.1,0)whereRisthe3monthLIBORrateatthebeginningofthequarter.45DerivativesCaps,Floors&Collars(Con’t)AfloorsetsalowerlimitontheinterestratewhichwillbechargedAcollarisboththepurchaseofacapandthesaleoffloor,oftenatnocosttothecorporate46DerivativesSwapsWhySwapsExistSizeofSwapsMarket47DerivativesWhySwapsExist...becausemarketsarenotperfect.Imperfectmarketsleadstofirmshavingcomparativeadvantagesindifferentmarkets.Ifeachfirmtransactsinthemarketwheretheyhaveacomparativeadvantage,anetbenefitwillbecreatedwhichcanbedividedbetweenthefirms.48DerivativesSizeofSwapsMarketTheuseofswapshasgrownexponentiallysincetheirfirstusein1981.Today,severaltrilliondollarsworthofthesecontractsareinexistence.Forexample,Table1andTable2showthesize,respectively,oftheInterestRateSwapsandCurrencySwapsMarketasofDecember31,1995.49DerivativesTable#1InterestRateSwapsSource:InternationalSwapsandDerivativesAssociationMarketSurvey,December31,199550DerivativesTable#2CurrencySwapsSource:InternationalSwapsandDerivativesAssociationMarketSurvey,December31,199551DerivativesBenefitsofUsingSwapsLowercostoffundsManageinterestrateexposureProvideaccesstointernationalcapitalmarketsHedgecurrencyexposureExtendorshortendebtmaturitiesChangetheinterestrateorcurrencysensitivityofassetsManageassetsandliabilitiesLockinfuturefinancingcostsDeferormatchcashflows52DerivativesDefinitionAswapisanagreementbetweentwopartiestoexchangefuturestreamsofpayments.Thetwobasictypesofswapsare:interestrateswapsandcurrencyswaps.53DerivativesAninterestrateswapisanagreementtoexchangeastreamofinterestpaymentsbasedononeinterestratebasisorindexforastreamofinterestpaymentsbasedonasecondinterestratebasisorindex,butwithbothstreamscalculatedbasedonthesamenotionalprincipalamount.InterestRateSwaps54DerivativesAcurrencyswapisanagreementtoexchange,overtime,aninterestflowdenominatedincurrencyAforaninterestflowdenominatedincurrencyB,withanexchangeofprincipalatthematuritydateoftheswap,withtheexchangeofprincipaldoneatafixedandpredeterminedexchangerate.CurrencySwaps55DerivativesTypesofSwaps56DerivativesSwapTerminology(1/2)ReceiverThecounterpartyreceivingthefixedinterestpaymentsPriceorswaprateThefixedinterestratepaidundertheswap(alsoreferredtoastheall-inswapprice)PayerThecounterpartymakingthefixedinterestpaymentsSwapspreadThedifferencebetweentheall-inswappriceandsomeacceptedbenchmarkrate,suchastheyieldonsimilarmaturitygovernmentbondscontinued-nextpage57DerivativesSwapTerminologyTradedateThedatethetermsoftheswapareagreedto.Alsoreferredtoasthefixingdate.ValuedateThedaythatintereststartstoaccrue.Maybeeitherthesameasthetradedate(fordomesticcurrency)ortwodaysafterthetradedate(forforeigncurrencies)RefixingdateThedaythatthefloatinginterestratesareresetEffectivedateThedatethatinterestfortheprecedingperiodispaid.ItmaybeequaltotheRefixingdate(fordomesticcurrency)ortwodayslater(forforeigncurrencies)58DerivativesComparingSwaps,Futures&Options59DerivativesSwapscanbeusedto...takeinterestrateriskhedgeagainstexistinginterestrateriskearnarbitrageprofitssynthesizeinstrumentswherenoneexistedbeforemanagethetimingofcash-flows60DerivativesUsingSwapstoTakeInterestRateRiskWecanuseswapsto:AssumeinterestrateriskwherenoneexistedbeforeORChangethenatureoftheinterestrateriskThreescenariosare:UsingswapsinisolationUsingswapstochangetheinterestrateriskofotherinstrumentsUsingswapstochangetheinterestrateriskofthebalancesheet61DerivativesSwap#1:ReceiveFixed,PayFloatingCounterpartyBankSwaps-CashFlowsCharacteristics:BankpaysFloatingBankreceivesFixedBankprofitsifInterestratesfallCashinstrumentsreplicatedBuyafixed-couponbondfundedwithfloatingratedeposits62DerivativesSwap#2:PayFixed,ReceiveFloatingCounterpartyBankSwaps-CashFlowsCharacteristics:BankpaysFixedBankreceivesFloatingBankprofitsifInterestratesriseCashinstrumentsreplicatedIssueafixed-couponbond.Investtheproceedsinafloatingrateasset.63DerivativesSwap#3:FixedRateAssetSwaps-CashFlowsCounterpartyAssetUsingSwapswithOtherInstrumentsBank64DerivativesSwap#4:FloatingRateAssetsSwaps-CashFlowsAssetBankCounterparty65DerivativesUsingSwapstoAdjusttheBalanceSheetIntheswapsabove......wehaveseenhowtochangetheinterestrateriskcharacteristicsofanexistingassetorliability,orsimplyassumeinterestrateriskwherenoneexisted.Next......whenanorganizationwantstoadjusttheinterestrateprofileofit’sbalancesheet.66DerivativesIfGAP=0Bank’’sinitialbalancesheetismatched,immunizingthebankfromadversechangesininterestrates.Preventsbankfromprofitingfromexpectedmovementsininterestrates.Cheapertouseinterestrateswapsthencashinstruments.RateSensitiveAssets-RateSensitiveLiabilities=GAPAdjustingGAP67DerivativesSwap#7:BalanceSheetAdjustmentsSwaps-CashFlowsCounterpartyAssetLiabilityBank68DerivativesSwap#8:BalanceSheetAdjustmentsSwaps-CashFlowsCounterpartyAssetLiabilityBank69DerivativesSwap#9:BalanceSheetAdjustmentsSwaps-CashFlowsCounterpartyAssetLiabilityBank70DerivativesSwap#11:HedgingSwaps-CashFlowsCounterpartyAssetLiabilityHedgingWithInterestRateSwapsBank71DerivativesSwap#13:BasisSwapSwaps-CashFlows6monthLIBOR3monthLIBOR6monthLIBOR3monthLIBORCounterpartyCounterpartyBankCounterparty72DerivativesArbitrageAgainstCashInstrumentsSwap#15:LiabilityArbitrageSwaps-ArbitrageLIBOR8.75%8.50%BankCounterpartyBondLiability73DerivativesWhySwapArbitrageOccursSwaparbitragecanoccurforseveralreasons:SwapslinkedtoanindexofaverageborrowingcostsSubsidizedfinancingSpeedatwhichnewinformationisincorporatedinto pricesSupplyanddemandimbalancesCreditornewissuearbitrage74DerivativesCurrencySwapssimilartointerestrateswaps(involveanexchangeofinterestrateflows)addtwoadditionalcomponentsinterestrateflowsarepaidindifferentcurrenciesexchangeofprincipalatthematuritydateoftheswap75DerivativesCurrencySwapsSterlinginterestflowsDollarinterestflowsSterlingprincipalflowDollarprincipalflowCompanyBCompanyA76DerivativesHedginganExistingCurrencyExposureCompanyAfromUKissuedabonddenominatedindollars,exposingittoexchangerisk.Toeliminatetheexchangeriskondollarbond,itentersintoacurrencyswapwithCo.Bwherebyitreceivesinterestdenominatedindollarsandpaysinterestdenominatedinsterling.Atthematuritydateoftheswap,Co.AwillpayCo.Bsterlingandreceivedollars(attheexchangeratefixedattheswapinitiationdate),whichitwillusetoredeemthebond.77DerivativesSampleSwapsQuestionAsabankmanager,youarefacedwiththefollowingproblem.CompanyAcanborrowfixedrateat8.0%andfloatingrateatLIBOR+25basispoints.CompanyBcanborrowfixedrateat9.0%andfloatingrateatLIBOR+50basispoints.CompanyAwantstohavefloatingratedebtandCompanyBwantstohavefixedratedebt.Theyhaveapproachedyou,thebankmanager,toseeifyoucouldhelpthemtoattaintheirdesiredtypesofdebtatalowercostthaniftheyweretofunddirectlyinthemarket.Ifyoudoso,youwouldliketomake5basispointsyourself.Whatwouldyoudo?AssumethatyouwillsplitanybenefitequallybetweenAandB(afteryougetyour5basispoints)78DerivativesSolutiontoSwapsQuestionCalculatethetotalnetbenefit,whichisequaltothedifferenceinthefixedratemarketminusthedifferenceinthefloatingratemarket.Fixedratemarket9.0%-8.0%=1.00%FloatingratemarketL+.50%-L+.25%=.25%NetBenefit.75%Deductfeetothebanker.05%BenefittobesplitbetweenA&B.70%BenefittoA(0.70%)(.50)=35bpBenefittoB(0.70%)(.50)=35bp79DerivativesCompanyABankCompanyBFixed@8%LIBOR+.50%LIBORLIBORFixed1Fixed2TocalculateFixed1:First,refertohowmuchCompanyAwouldhavetopayifitborrowedfloatingratemoneydirectlyinthemarket.ThendeductthenetbenefitduetoAundertheswap.ThisisA’’s‘‘allincost’’offinancing.Thisisequaltothesumof:LIBOR(paidbyAunderthefloatinglegoftheswap)plusthespreadinthefixedlegoftheswap.SolutiontoSwapsQuestion80DerivativesSolutiontoSwapsQuestionOnthepreceedingpage,wesolvedforthefixedpaymentreceivedbyCompanyA(Fixed1).ThereisanalternativewaytosolvetheswapsproblemusingasimplerelationshiptosolveforthefixedpaymentmadebyCompanyB(Fixed2).Itis:NetLIBORcosttoB(LIBORout-LIBORin)+X(theunknownfixedpaymentmadebyCompanyB)=FixedrateifBborroweddirectlyinthemarket-B’’sproportinatebenefitundertheswap.SolveforX.81DerivativesSampleSwapsQuestionYouarefacedwiththefollowingsituation.CompanyFixedRateFloatingRateABCCompany6.0%LIBOR+1/8%XYZCompany7.35%LIBOR+3/8%Questions:Whatisthetotalnetbenefittodoingaswap?WhichcompanyhasthecomparativeadvantageinthefloatingratemarketConstructaswapwherebythebankergets10basispointsandtheremainingbenefitissplit75%toABCand25%toXYZ.82DerivativesSolutiontoSwapsQuestionCalculatethetotalnetbenefit,whichisequaltothedifferenceinthefixedratemarketminusthedifferenceinthefloatingratemarket.Fixedratemarket7.35%-6.00%=1.35%FloatingratemarketL+3/8%-L+1/8%=.25%NetBenefit1.10%Deductfeetothebanker.10%BenefittobesplitbetweenABC&XYZ1.00%BenefittoABC(1.00%)(.75)=75bpBenefittoXYZ(1.00%)(.25)=25bp83DerivativesABCBankXYZFixed@8%LIBOR+3/8%LIBORLIBORFixed1Fixed2TocalculateFixedA:First,refertohowmuchABCwouldhavetopayifitborrowedfloatingratemoneydirectlyinthemarket.ThendeductthenetbenefitduetoABCundertheswap.ThisisABC’’s‘‘allin’costoffinancing.Thisisequaltothesumof:LIBOR(paidbyABCunderthefloatinglegoftheswap)plusthespreadinthefixedlegoftheswap.SolutiontoSwapsQuestion84DerivativesSolutiontoSwapsQuestionOnthepreceedingpage,wesolvedforthefixedpaymentreceivedbyABC(Fixed1)ThereisanalternativewaytosolvetheswapsproblemusingasimplerelationshiptosolveforthefixedpaymentmadebyXYZ(Fixed2).Itis:NetLIBORcosttoXYZ(LIBORout-LIBORin)+X(theunknownfixedpaymentmadebyXYZ)=FixedrateifXYZborroweddirectlyinthemarket-XYZ’’sproportinatebenefitundertheswap.SolveforX.85DerivativesSampleOptionProblemsYouareacallbuyerfacingthefollowing:Callpremium$1.50Exerciseprice$25.00Stock’’smarketpriceatexpirydate$24.50a) Whatisthebreakevenstockpricerequiredb) Whatistheprofitorlosstothecallbuyerc) Underwhatmarketconditionswouldyoubuyacall?Youareacallwriterfacingthefollowing:Callpremium$2.00Exerciseprice$20.00Stock’’smarketpriceatexpirydate$21.00a) Whatisthebreakevenstockpricerequiredb) Whatistheprofitorlosstothecallwriterc) Underwhatmarketconditionswouldyouwriteacall?86DerivativesSampleOptionProblemsYouareaputbuyerfacingthefollowing:Putpremium$3.00Exerciseprice$15.00Stock’smarketpriceatexpirydate$10.00a) Whatisthebreakevenstockpricerequiredb) Whatistheprofitorlosstotheputbuyerc) Underwhatmarketconditionswouldyoubuyaput?Youareaputwriterfacingthefollowing:Putpremium$2.00Exerciseprice$20.00Stock’smarketpriceatexpirydate$21.00a) Whatisthebreakevenstockpricerequiredb) Whatistheprofitorlosstotheputwriterc) Underwhatmarketconditionswouldyouwriteaput?87DerivativesSampleOptionProblemsYouareacoveredcallwriterfacingthefollowing:Putpremium$3.00Callpremium$2.00PutExerciseprice$15.00CallExerciseprice$15.00Stock’’spriceatoption’’sinitiationdate$15.00Stock’spriceatoption’sexpirydate $14.00a)Whatistheprofitorlosstothecoveredcallwriter?b)Whymightyouwanttowritecoveredcalls?C)Underwhatmarketconditionswouldyouwritecoveredcalls?Note:Youmaynotneedtousealltheinformationprovidedtosolvethisproblem:88DerivativesSwapsProblem-Commerzbankvs.PeregrineTheIssue-CommerzbankofGermanyhaslaunchedasuitagainstPeregrine,theAsianInvestmentBankthatfailedJanuary9,1998,allegingthatPeregrinenew,orshouldhaveknown,thatitwasclosetofailureatthetimethatitenteredintoacurrencyswapwithCommerzbank.CommerzbankclaimsthatwhenPeregrinedirectorsenteredtheswapdealandreceiveditspaymentofDM73Million(US$41.2Million),theyshouldhaverealizedtheywereclosetocollapseandunabletofulfiltheircounterpartypaymentofUSdollarswhenNewYorkopened.Thecasewillraisequestionsa