1.第一節(jié)講義-簡介Derivatives-1-MFIN-Introduction

MFIN6003DerivativeSecuritiesLectureNoteOneHKUBusinessSchoolUniversityofHongKongDr.HuiyanQiu1-1OutlineCourseOverviewIntroductiontoDerivativesWhatisaderivative?Derivativesmarkets“Review”onBasicsBondandequity/stockTimevalueofmoneyBasictransactionsincludingshort-sellingNo-arbitrageprincipleReading:McDonaldChapter11-2OverviewoftheCourseThecourseisabout:theconcept,theuse,andthepricingofbasicderivatives.IntroductiontoderivativesingeneralIntroductiontoforwardandfutures;FuturestradingPricinganduseofforwardandfuturesCurrencyforwardandfutures;Interestrateforwardandfutures1-3OverviewoftheCourse(cont’d)SwapsIntroductiontooptionsandoptionstrategiesincludingbasisriskmanagementOptionpricepropertiesBinomialoptionpricingmodelBlack-Scholesformulaanddelta-hedging1-4OutlineCourseOverviewIntroductiontoDerivativesWhatisaderivative?Derivativesmarkets“Review”onBasicsBondandequity/stockTimevalueofmoneyBasictransactionsincludingshort-sellingNo-arbitrageprincipleReading:McDonaldChapter11-5WhatareDerivatives?Aderivativesecurityisafinancialinstrumentwithvaluederivedfromsomeunderlyingasset(s)whosepricesaretakenasgiven.Example:28Sep2023-60.00CallonHSBCAcalloptionthatgivesthesecurityholdertherighttopayHK$60persharetobuy400sharesofHSBCstockbySeptember28,2023.AsofJuly24,2023,thepricesoftheoptionandtheHSBCstockare$4.65and$64.00,respectively.1-61-7Optionpriceisdeterminedbyseveralfactorsincludingthepriceoftheunderlyingasset.Weexaminehowtousederivativecontractstodealwithfinancialrisksrelatedto:–Stockprices–Commodityprices–Exchangerates–Interestrates1-8Figure:2009ISDADerivativesUsageSurvey:TypesofRiskManagedusingDerivatives(%)BasicTypesofDerivativesForwardcontractsandfuturescontractsareagreementstobuyorsellanassetatacertainfuturetimeTforacertainpriceK.Swapsaresimilartoforwards,exceptthatthepartiescommittomultipleexchangesatdifferentpointsintime.AcalloptiongivestheholdertherighttobuytheunderlyingassetbyacertaindateTforacertainpriceK.AputoptiongivestheholdertherighttoselltheunderlyingassetbyacertaindateTforacertainpriceK.1-9AnExampleYouenteranagreementwithafriendthatsays:Ifthepriceofabushelofcorninoneyearisgreaterthan$6,youwillpayhim$1,000Ifthepriceislessthan$6,hewillpayyou$1,000ThisagreementisaderivativecontractQuestions:Whathappensoneyearlater?(outcome,carry-out)Whydoyouoryourfriendwanttoenterthisagreementatthefirstplace?Cornpriceovertimeisshownonthenextslide.1-10CornPricesinceJan2021Source:1-11UsesofDerivativesRiskmanagementHedging:wherethecashflowsfromthederivativeareusedtooffsetormitigatethecashflowsfromapriormarketcommitment.SpeculationWherederivativeisusedwithoutanunderlyingpriorexposure;theaimistoprofitfromanticipatedmarketmovements.ReducetransactioncostsRegulatoryarbitrage1-12

ObserversEnduserEnduserIntermediaryEconomic

ObserversRegulatorsResearchersThreeDifferentPerspectivesEndusersCorporationsInvestment

managersInvestorsIntermediariesMarket-makersTraders1-13HistoryofderivativesDerivativesMarketsTheexchangemarket:anorganizationthatprovidesavenuefortradingandsetsrulesgoverningwhatistradedandhowtradingoccurs.Aclearinghousematchesthebuyersandsellers,keepingtrackoftheirobligationsandpaymentsFuturescontracts,mostoptionsTheover-the-counteror“OTC”market:wheretwopartiesworkdirectlywitheachothertoformulate,execute,andenforceaderivativetransaction.Forwardcontracts,mostswaps1-14ExchangeTradedContractsContractsproliferatedinthelastseveraldecades

ExamplesofunderlyingassetsonwhichfuturescontractsaretradedinUSWhatwerethedriversbehindthisproliferation?1-15IncreasedVolatility…Oilprices:1947–2011*Dollar/Poundrate:1947–2011

*1-16…LedtoNewandBigMarketsFigure:CombinedfuturescontracttradingvolumeforthethreelargestU.S.futuresexchangefrom1970to2011.1-17Figure:

SizeofOver-the-CounterandExchange-TradedDerivativesMarketsbetween1998and2016.1-18DerivativesProductsinHKDerivativesproductslistedinHKExincludefuturesandoptionsonthefollowingunderlying:EquityIndexSingleStockForeignExchangeInterestRate(Futuresonly)

Commodities(Futuresonly)Weblink:.hk/Figure:ContractvolumeoffuturesandoptionsinHK,2000-2022.1-19Source:.hk/DerivativesProductsinHK(cont’d)StructuredproductslistedinHKExinclude:DerivativeWarrants(DW)CallableBull/BearContracts(CBBC)InlineWarrants(IW)OTCmarketproducts:numerousCurrentlyOTCClearclearsinterestrateswaps(IRS),Northboundinterestrateswaps(NBIRS),non-deliverablecurrencyforwards(NDF),crosscurrencyswaps(CCS)anddeliverableFX(DFX)..hk/Products/OTC-Derivatives/Eligible-OTC-Clear-Products?sc_lang=en

1-20FuturesExchangesinChinaDalianCommodityExchange(1993.02):/ZhengzhouCommodityExchange(1998.08):/ShanghaiFuturesExchange(1999.12):/ChinaFinancialFuturesExchange(2006.09):/GuangzhouFuturesExchange(2021.04):

/OTCmarketproducts:numerous1-21OutlineCourseOverviewIntroductiontoDerivativesWhatisaderivative?Derivativesmarkets“Review”onBasicsBondandequity/stockTimevalueofmoneyBasictransactionsincludingshort-sellingNo-arbitrageprincipleReading:McDonaldChapter11-22BondBasicsAbondisafixed-incomeinstrumentthatrepresentsaloanmadebyaninvestortoaborrower(typicallycorporateorgovernmental).Bondsareusedbycompanies,municipalities,states,andsovereigngovernmentstofinanceprojectsandoperations.Ownersofbondsaredebtholders,orcreditors,oftheissuer.Investopedia:WhatIsaBond?1-23EquityBasicsAstock,alsoknownasequity,isasecuritythatrepresentstheownershipofafractionoftheissuingcorporation.Corporationsissuestocktoraisefundstooperatetheirbusinesses.Stocksareboughtandsoldpredominantlyonstockexchangesandarethefoundationofmanyindividualinvestors'portfolios.Investopedia:WhatAreStocks?1-24TimeValueofMoneyTimevalueofmoneyreferstoadollartodayisdifferentfromadollarinthefutureTimevalueofmoneyismeasuredbytheinterestratefortheperiodconcerned.Tocomparemoneyflows,wemustconvertthemtothesametimepoint.Whichoneismorevaluable?$100$1101-25FutureValueandPresentValuewhereFV=futurevalue PV=presentvalue r=thequotedannualinterestrate m=thenumberoftimesinterestis compoundedperyear n=thenumberofcompoundingperiodsto maturity1-26ASimpleExample$100isdepositedforayearatquotedannualpercentagerate(APR)of12%withmonthlycompounding.Given12%APR,themonthlyinterestrateis1%.Attheendofeachmonth,interestiscalculatedandaddedtotheprincipletoearnmoreinterest.Endofmonth1:$100(1+1%)Endofmonth2:$100(1+1%)(1+1%)=100(1+1%)2:Endofmonth12:$100(1+1%)12=$100(1+12.68%)12.68%istheeffectiveannualrate(EAR).1-27APRandEARAPR:annualpercentagerateEAR:effectiveannualrateCompoundingFrequencynEAR(%p.a.)Annually112.0000Quarterly412.5509Monthly1212.6825Weekly5212.7341Daily36512.7475Continuously∞12.7497APR=12%1-28ContinuouslyCompoundingContinuouslycompounding:n→∞(infinity)APR=12%

EAR=12.75%At12%continuouslycompoundingannualinterestrate,thefuturevalueof$100is$112.75.1-29In-ClassExerciseIAninterestrateisquotedas5%perannumwithsemiannualcompounding.Toresultinthesameeffectiverate,whatshouldbetheannualpercentagerateifannualcompounding?monthlycompounding?continuouscompounding?1-30In-ClassExerciseIIYourgrandparentsputsomemoneyinanaccountforyouonthedayyouwereborn.Youarenow22yearsoldandareallowedtowithdrawthemoneyforthefirsttime.Theaccountcurrentlyhas$23,699initandpaysa4%effectiveannualinterestrate.Howmuchmoneywouldbeintheaccountifyouleftthemoneythereuntilyour32ndbirthday?65thbirthday?Howmuchmoneydidyourgrandparentsoriginallyputintheaccount?1-31In-ClassExerciseIIIConsideracorporatebondwiththreeyearstomature.Thebondpayscouponsemi-annuallywithcouponrate4%peryear.(Thebondholdergets$2everysixmonthsper100facevalue.)Ifthebondisyielding5%peryear.Whatisthepriceofthebond?1-32OutlineCourseOverviewIntroductiontoDerivativesWhatisaderivative?Derivativesmarkets“Review”onBasicsBondandequity/stockTimevalueofmoneyBasictransactionsincludingshort-sellingNo-arbitrageprincipleReading:McDonaldChapter11-33BasicTransactionsAtransactionisacompletedagreementbetweenabuyerandasellertoexchangegoods,services,orfinancialassetsinreturnformoney.Transactioncostsarethepaymentsthatbanksandbrokersreceivefrombuyersandsellersfortheirroles.Brokers:commissionsfees(servicecharge)Market-makers:bid-askspread(thedifferencebetweentheask/offerpriceandbidprice)1-34BasicTransactions:ExampleOneyearago,Ellenpurchased100sharesofXYZstockwhenthestockpricepersharewas$49.75(bid)and$50(offer).Ellenpaid$15ascommissions.Today,Ellensellsallthestockswhenthestockpricepershareis$52.25(bid)and$52.5(offer).Ellenpays$15ascommissionsfortheselling.Supposetheeffectiveannualinterestrateis3%andXYZstockdoesnotpaydividendovertheyear.WhatisEllen’sprofit?1-35Short-SellingShort-sellingisatradingstrategyinwhichaninvestorborrowsasecurityandsellsitontheopenmarket,planningtobuyitbacklaterforlessmoney.Whathappensifpricedoesn’tfallasexpected?Theriskoflossistheoreticallyunlimited.***Short-sellingisanadvancedstrategythatshouldonlybeundertakenbyexperiencedtradersandinvestors.Iftheassetpaysdividendinbetween,whogetsthedividendpayment?1-36Short-Selling(cont’d)Example:Cashflowsassociatedwithshort-sellingashareofHSBCfor90days.Notethattheshort-sellermustpaythedividend,D,totheshare-lender.Inotherwords,thelendermustbecompensatedforthedividend.1-37Short-Selling(cont’d)Whyshort-sell?SpeculationHedgingCreditriskinshort-sellingCollateral:saleproceeds+possibleextraamountrequired(calledhaircut)InterestreceivedfromlenderoncollateralwhenassetisreturnedScarcitydecreasestheinterestrateThedifferencebetweenthisrateandthemarketrateofinterestisanothercosttoyourshort-sale1-38ExampleAssumethatyouopena100sharepositioninFanny,Inc.commonstockatthebid-askpriceof$32.00-$32.50.Whenyoucloseyourpositionthebid-askpricesare$32.50-$33.00.Youpayacommissionrateof0.5%.WhatisyourprofitorlossifCase1:youpurchasethestockthensell;Case2:youshort-sellthestockthenclosetheposition.1-39Example(cont’d)Youpayaskpricewhenyoupurchaseastockandyougetbidpricewhensellingastock.Ifthemarketinterestrateiszero,Case1:lossof$32.50Case2:lossof$132.50Iftheeffectivemarketinterestrateoveryourholdingperiodis2%,Case1:lossof$97.825Case2:lossof$68.821-40DiscussionQuestion1:Withzerointerestrate,whythelossinshort-sellingismorethanthelossinoutrightpurchase?Question2:Interestrateseemstohavepositiveeffectontheprofit/lossonshort-sellingbutnegativeeffectontheprofit/lossonoutrightpurchase.Reason?Question3:Atwhatinterestrate,profit/lossfromshort-sellingorfromoutrightpurchaseisthesame?1-41OutlineCourseOverviewIntroductiontoDerivativesWhatisaderivative?Derivativesmarkets“Review”onBasicsBondandequity/stockTimevalueofmoneyBasictransactionsincludingshort-sellingNo-arbitrageprincipleReading:McDonaldChapter11-42PricingApproachesIngeneral,therearetwoapproachestopriceanasset(oracontractoraportfolio):DCFpricingapproachandno-arbitragepricingapproach.PricinganassetusingDCFapproach:DeterminecashflowsandtheirriskUsesometheoryofinvestor’sattitudetowardsriskandreturn(e.g.,CAPM)tofigureouttheexpectedorrequiredrateofreturnConductdiscountedcashflowanalysistofindthepresentvalueoffuturecashflows1-43DCFPricingApproach:Example

1-44No-ArbitragePricingApproachPricingofderivativesoftenuseno-arbitrageargument.Arbitrageisanytradingstrategyrequiringnocashinputthathassomeprobabilityofmakingprofits,withoutanyriskofalossCanoneexpecttocontinuallyearnarbitrageprofitsinwellfunctioningcapitalmarkets?Fromaneconomicperspective,theexistenceofarbitrageopportunitiesimpliesthattheeconomyisinaneconomicdisequilibrium.1-45LawofNoArbitrageLawofNoArbitrage:aportfolioinvolvingzerorisk,zeronetinvestmentandpositiveexpectedreturnscannotexist.LawofOnePrice:

twoequivalentthingscannotsellfordifferentprices.Assumptions:

Nomarketfrictions(transactioncosts?bid/askspread?restrictiononshortsales?taxes?)Nocounterpartyrisk(creditrisk?collateralrequirements?marginrequirements?)Competitivemarket(liquidityconcern?)1-46ExampleI:PortfolioValuationFollowingisthepayoffandno-arbitragepricesofsecuritiesAandB:WhatisthepayoffofaportfolioofoneshareofsecurityAandoneshareofsecurityB?Whatisthemarketpriceofthisportfolio?Whatistheeffectiverisk-freerateofreturn?1-47CashFlowinOneYearSecurityPriceTodayWeakEconomyStrongEconomySecurityA230.770600SecurityB346.776000Example(cont’d)

1-48Example(cont’d)NowconsidersecurityCthathasapayoffof$600whentheeconomyisweakand$1,800whentheeconomyisstrong.Whatistheno-arbitragepriceofsecurityC?Solution:ThecashflowsofsecurityCcanbereplicatedbythreesharesofsecurityAandoneshareofsecurityB.Therefore,theno-arbitragepriceofsecurityCis$230.77×3+$346.77=$1,039.08.1-49Example(cont’d)IfsecurityCisnotsellingfor$1,039.08,thereexistsarbitrageopportunities.Forexample,securityCissellingfor$1,200.Arbitragepositions:

ShortselloneshareofsecurityCBuythreesharesofsecurityABuyoneshareofsecurityBTime-0cashflow:$1,200–$1,039.08=$160.92Oneyearlater,thepayofffromthreesharesofAandoneshareofBoffsetsthepayoffforC.1-50ExampleII:ArbitrageProfitSupposethefollowingthreebondsareavailableinthemarkettobuyandtosell.BondA,whichpays$100inoneyear,costs$95today.BondB,whichpays$10inyear-1and$110inyear-2,costs$100today.BondC,whichpays$5inyear-1and$105inyear-2,costs$90today.Question:Ignoringthetransactioncost,anyfreemoney/arbitrageprofit?Howtomaketheprofit?1-51No-ArbitragePricingMethodAnotherExample:

CurrentstockpriceS0=$25.00,thereisnodividendspaymentinthefollowing6monthsThecontinuouslycompoundingrisk-freeannualinterestrate=7.00%Acontract(forwardcontract):agreementtobuythestockattime6forF0,6=$26.00(forwardprice)Istherearbitrageprofittomake?(Istheforwardcontractfairly-priced?)1-52Example(cont’d)Howtogenerateaportfolio(syntheticcontract)whichduplicatesthecashflows

andvalueofthecontractunderconsiderationCashflowsoftheforwardcontract:Time0:ZeroTime6:Outflowof$26andinflowofS6

attime6(valueofthecontract:S6

–26.)Syntheticcontract:borrow$25.00tobuythestockTime-0cashflow:Zero1-53Example(cont’d)Attime6,Syntheticcontract:paybacktheborrowedmoneyandstillhavethestock.Payment:25[e(.07)(6/12)]=

25.89Forwardcontract:pay$26.00tohavethestockConclusion:thecontractisover-priced!Sellthecontract!(Shortthecontract!)Atthesametime,

buy(long)thesyntheticcontract!1-54Example(cont’d)AtTime0(Cash)Borrow$25.00ata7.00%annualratefor6monthsBuythestockat$25.00Writetheforwardat $26.00Between0and6(Carry)Attime6Paybackborrowedmoney:

25[e(.07)(6/12)]=

25.89Get$26.00fromtheforward(andgiveupthestock)Netpayoff:$0.111-55LearnfromtheExampleArbitrage-freeforwardprice:F0,T=S0erTForwardpriceisthedeferredvalueofthespotpriceThedeferredrateistherisk-freerateQuestion:

S0=$25.00;F0,6=$25.50Thecontinuouslycompoundedrisk-freeannualinterestrate=7.00%Whatarbitragewouldyouundertake?Howtomakeprofit?1-56EndoftheNotes!1-57After-ClassExerciseAninvestorreceives$1,100inoneyearinreturnforaninvestmentof$1,000now.Calculatethepercentagereturnperannumwith:(a)AnnualCompounding,(b)SemiannualCompounding,(c)MonthlyCompounding,and(d)ContinuousCompounding.Answer:10.00%;9.76%;9.57%;9.53%.Ifyouneed€15,000inthreeyears,howmuchwillyouneedtodeposittodayifyoucanearn8percentperyearcompoundedcontinuously?Answer:€11,799.421-58SupposeBankOneoffersarisk-freeinterestrateof5.5%onbothsavingsandloans,andBankEnnoffersarisk-freeinterestrateof6%onbothsavingsandloans.Theinterestratesofferedbythetwobankshavesamecompoundingfrequency.Whatarbitrageo