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1、S-MBle-US roQ SuI-BOIU OJOwluo。OUO-eo17 SlU IUl-EE0。PBMOL1_OU-2-BPUB M一 6m TO MraPUeuo=en-e:SUlEls*3e:寸1SSWeulOOi:Sesosvos- SsTOMil扈andValuationofForwardCommitmentsPricingandvaluationofforwardcommitmentsPricingofforwardPricingoffuturesValuationofforwardPricingofswapValuationofswapPricingofForwardPri
2、cingofforwardIftheunderlyinggeneratesnoperiodiccashflow:F0(T)=S0(l+r)IfF(7)Sy,+r):Cash-and-CarryarbitrageAtinitiation:borrowmoneySgtR,fbuythespotasset,andselltheforwardatF0(T).Atexpiration:settletheshortpositiononforwardcontractbydeliveringtheasset.Profitatexpiration:Fq)-SQ+r)LPricingofForwardPricin
3、gofforward(Cent.)IfFg)Sy.+r)T:ReverseCash-and-CarryarbitrageAtinitiation:borrowandsellthespotasset,investtheproceedS0atRpandbuytheforwardatF0(T).Atexpiration:payFJ)tosettlethelongpositiononforwardcontract,anddeliverthespotassettoclosetheshortpositiononspotasset.Profitatexpiration:S(jl+r)-F(J).Pricin
4、gofForwardPricingofforward(Cont.)Iftheunderlyinggeneratesperiodiccashflow:F0(T)=(S0-+)(lr)Pricingofequityforwardwithdiscretedividend:F0(T)=(S0-PVD0)(lr)or:Fd(T)=So(lr)-FVDPricingofequityindexforward:continuousdividend(c)F0(T)=SoXRj-fic)Pricingoffixedincomeforward:discretecouponF0(T)=(S0-PVC0)X(l+r)o
5、r:F0(T)二S0X(l+r)-FVCPricingofForwardPricingofforward(Cont.)PricingofFRA:Theunbiasedestimateofforwardrate,calculatedfromthespotrates(forwardratemodel).Pricingofcurrencyforward:1+RdcJ良兄(T)=SX-or:F(T)=SXe(RDCRFC)T十00、FCOL。(tw瞬三s悟大情太遇打m一ETW瞬三selx眯#匿Owi三-il-oDX盗虫经二+d父朕持赞。w玄W国一(、厘匾楹ss-aws。碘既海胆三-i三s三-sssss
6、S黑胆离US工袈藤屈一peM0MU-d三nsPractice1JimTrent,CFAhasbeenaskedtopriceathreemonthforwardcontracton10,000sharesofGlobalIndustriesstock.Thestockiscurrentlytradingat$58andwillpayadividendof$2today.Iftheeffectiveannualrisk-freerateis6%,whatpriceshouldtheforwardcontracthave?Assumethestockpricewillchangevalueafte
7、rthedividendispaid.A)$55.85.B)$58.85.C)$56.82.Practice1Answer:CF(T)=(58-2)*(l+6%)1/4=$56.82OPricingofFuturesPricingoffixedincomefuturesQuotedfuturesprice=(SGPVC)X(l+r)-AlCF二S0(l+r)-Al-FVCCFS亍QUotedPriCe+Al0Al=-PMTT-tPMTPMT+FIIIIOsettlement1ndateValuationofForwardValuationofforwardValueofforward:thed
8、ifferencebetweenzzwiththepositionandwithouttheposition.Generallydefinevalueasthevaluetothelongposition.Atinitiation(t=0):VO(T)=0.Duringitslife(tPBMOJEoUU-PX匚O-ro一UA,27x-=，T匕111(Eszl2dIS)M(Iy:PJPMOJo-roH二UOJ)peMoMoUo4e=e三三0Sesras-SValuationofForwardValuationofforward(Cont.)Thevalueofcurrencyforward:V
9、t(T)=St(l+RpcM-F0(T)X(1+RdcMForcontinuouslycompoundedrisk-freerate:Vt(T)=Ste-Rfc(T-1)-F0(T)-rdc-1(ValuationofForwardValuationofforward(Cont.)ThevalueofFRAatexpiration(t=a): DayS)I 360 JUsesimpleinterestformoneymarketinstrument.NPx(Underlyingrate-Forwardrate)x01UnderlyingrateaDaySII360IbValuationofFo
10、rwardValuationofforward(Cont.)ThevalueofFRApriortoexpiration(ta):Step1:calculatethenewFRArate(FR)t1Sblbt1Sa：t1FRtaStep2:calculatethevalueofFRAas:NPx(FR,一FR。)(DayS既atob)j吓DaySfrOmttObj%C360J0tabPractice1TheU.S.risk-freerateis2.96%,theJapaneseyenrisk-freerateis1.00%,andthespotexchangeratebetweentheUni
11、tedStatesandJapanis$0.00757peryen.Bothratesarecontinuouslycompounded.Thepriceofa180-dayforwardcontractontheyenandthevalueoftheforwardposition90daysintothecontractwhenthespotrateis$0.00797areclosestto:Forward PriceA) $0.00764B) $0.00764C) $0.00750Value After 90 Days$0.00212$0.00037$0.00212Answer:BF(T
12、)=$0.00757e(0.0296-o.ooo)(iso/365)=$0.00764oV(T)=0.00797-o.o.(90/365)-0.00764xe-0.0296.(90/355)=$0.0003706TgI9sO8lnm6(8oss(V:。1Issop-IUnoHJ-Hog-!ABP06IU8n。El6IBp&JdPUe(mo-l)SBHPuoUBGPWU-UopuolUoPcSBqUo0-B-IUoIl三MEoccouOUoABn-e三三m三sIous三三MBinomialOptionValuationModelOne-periodbinomialmodelDiagramillu
13、stration:S0Co = (TlUXC+%XC-)/(1+ Rf?C+=Max(0,S+-X)P+=Max(O,X-S+)C-=Max(O,S-X)P-=Max(0,X-S-)P0=(uP+0P-)(l+Rf)11=(1+RD)(U-D)risk-neutralprobabilityofup-move;Rty1-R(UriSk-neutralprobabilityofdown-move.Two-periodbinomialmodelforEuropeanoptionC-=Max(0,S-X)P-=Max(0,X-S-)BinomialOptionValuationModelTwo-per
14、iodbinomialmodelforEuropeanoption(Cont.)CalculationofC+andP+,C-andP-:C=(C+RC+-)/(1+RPC-=(r3C-+11RC-)(1+RFP=(h王P+RRP-)/(1+RP-=(r卞P+-+R存P-)/(1+RPCalculationofCndPC(calculatedprice,selltheoptionandbuyhsharesofthestockforeachoptionwesold;Ifmarketprice0-s01sJoroooocJoa-一lSJJO=一M-8ooossJoUo-sodto-1.3一3dIn
15、gRiskExposuresInterestrateswapFixed-ratereceiver:increaseduration;Fixed-ratepayer:decreaseduration.Interestratefutures1.onginterestratefutures:increaseduration;Shortinterestratefutures:decreaseduration.Stockindexfutures1.ongstockindexfutures:increasetheequityexposure;Shortstockindexfutures:decreaset
16、heequityexposure.IngRiskExposuresEquityswapEquityswapcanbeusedtomodifyexposuretoequitymarkettemporarilywithoutactuallydisposingtheequityportfolio.CurrencyswapCurrencyswapareusuallyusedbycompaniestoreducetheirfundingcosts.Currencyforward/futuresCurrencyforward/futurescanbeusedtomanageforeignexchanger
17、aterisk.etic EquivalenciesSyntheticassetwithoptions1.ongasset=longcall+shortput(S=C-P)Shortasset=shortcall+longput(-S=-C+P)Syntheticoptions1.ongcall=longasset+longput(C=S+P)1.ongput=Shortasset+longcall(P=-S+C)Syntheticassetwithforward/futures1.ongasset=longfutures+risk-freeasset(cash)DerivativeStrat
18、egiesCoveredcall(S-C)Investmentobjectives:IncomegenerationImprovingonthemarketTargetpricerealizationRiskofcoveredcall:Keepsthedownsideriskofthestockposition;Givesuptheupsidepotentialofthestockposition.DerivativeStrategiesProtectiveput(S+P)Investmentobjectives:Provideprotectionorinsuranceagainstapric
19、edecline.Riskofprotectiveput:Theputpremiumwillreducetheportfolioreturn.DerivativeStrategiesCoveredcallvs.(longasset+shortforward)Fromtheaspectofdelta,acoveredcallpositionisequivalenttoapositionof(longastock+shortforwardfordetalcaunit).Bothofthemhavedeltaof(1-deltacJtProtectiveputvs.(longasset+shortf
20、orward)Fromtheaspectofdelta,aprotectiveputpositionisequivalenttoapositionof(longastock+shortforwardfordetalputunit).Bothofthemhavedeltaof(1+deltaptDerivativeStrategiesSpreadstrategyBullspread:longanoptionandshortanotherwithahigherexerciseprice;BullcallspreadBullputspreadBearspread:longanoptionandsho
21、rtanotherwithalowerexerciseprice;BearcallspreadBearputspreadDerivativeStrategiesCollarStructure:longput+shortcall+underlyingassetInvestmentobjective:buyaprotectiveputandsellacalltooffsetthepremium.Zero-costcollar:thepremiumsforcallandputareequal.Straddle1.ongstraddle:Longcall+longput,withthesameexer
22、ciseprice,onthesameunderlyingasset.1.ongvolatility.DerivativeStrategiesChoiceofderivativestrategiesForexpectationofmarketdirection,typically:1.ongcall/put:strongbullish/bearishexpectation;1.ongcall+shortput:averagebullishexpectation;Shortcall+longput:averagebearishexpectation;Writingcall/put:weakbearish/bullishexpectation.Forexpectationofvolatility,typically:1.ongstraddle:highvolatilityexpectation;Shortstraddle:lowvolatilityexpectation.
