CFA二级复习冲刺-衍生.docx
S-MBle-US >ro>Q SuI-BOIU OJOwluo。OUO-e>o17 SlU IUl-EE0。PBMOL1_OU-2-B>PUB M一 6m TO MraPUeuo=en-e>:SUlEls>>*3e:寸1SSWeulOOi:Sesosvos- SsTOMil扈andValuationofForwardCommitmentsPricingandvaluationofforwardcommitmentsPricingofforwardPricingoffuturesValuationofforwardPricingofswapValuationofswapPricingofForwardPricingofforwardIftheunderlyinggeneratesnoperiodiccashflow:F0(T)=S0×(l+r)IfF(7)>Sy,+r):Cash-and-CarryarbitrageAtinitiation:borrowmoneySgtR,fbuythespotasset,andselltheforwardatF0(T).Atexpiration:settletheshortpositiononforwardcontractbydeliveringtheasset.Profitatexpiration:Fq)-SQ+r)LPricingofForwardPricingofforward(Cent.)IfFg)<Sy.+r)T:ReverseCash-and-CarryarbitrageAtinitiation:borrowandsellthespotasset,investtheproceedS0atRpandbuytheforwardatF0(T).Atexpiration:payFJ)tosettlethelongpositiononforwardcontract,anddeliverthespotassettoclosetheshortpositiononspotasset.Profitatexpiration:S(jl+r)-F(J).PricingofForwardPricingofforward(Cont.)Iftheunderlyinggeneratesperiodiccashflow:F0(T)=(S0-+)(l÷r)Pricingofequityforwardwithdiscretedividend:F0(T)=(S0-PVD0)×(l÷r)or:Fd(T)=So×(l÷r)-FVDPricingofequityindexforward:continuousdividend(c)F0(T)=SoXRj-fic)Pricingoffixedincomeforward:discretecouponF0(T)=(S0-PVC0)X(l+r)or:F0(T)二S0X(l+r)-FVCPricingofForwardPricingofforward(Cont.)PricingofFRA:Theunbiasedestimateofforwardrate,calculatedfromthespotrates(forwardratemodel).Pricingofcurrencyforward:1+Rdc'J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Ow×i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-sssssS黑胆离US工袈藤屈一peM£0MU-d三nsPractice1JimTrent,CFAhasbeenaskedtopriceathreemonthforwardcontracton10,000sharesofGlobalIndustriesstock.Thestockiscurrentlytradingat$58andwillpayadividendof$2today.Iftheeffectiveannualrisk-freerateis6%,whatpriceshouldtheforwardcontracthave?Assumethestockpricewillchangevalueafterthedividendispaid.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:thedifferencebetweenzzwiththeposition"and"withouttheposition".Generallydefinevalueasthevaluetothelongposition.Atinitiation(t=0):VO(T)=0.Duringitslife(t<T):Vt(T)=(St-t+t)-F0(T)(l÷r)-(-t)=Ft(T)-F0(T)(l+r)-(-t)Atexpiration(t=T):V(T)=S-F0(T)(ED×(T三UT(E)×(I)OLL'，gdIS)U(1>PBMOJEoUU-PX匚O-ro>一UA,27<x-=，T匕<×s"-L)A-PJBM0JxpwAI-nbo-ro>111(Eszl2>dIS)M(Iy>:PJPMOJo-ro>H二UOJ)peMoMoUo4e=e>三三0Sesras-SValuationofForwardValuationofforward(Cont.)Thevalueofcurrencyforward:Vt(T)=St×(l+RpcM-F0(T)X(1+RdcMForcontinuouslycompoundedrisk-freerate:Vt(T)=St×e-Rfc(T-1)-F0(T)×-rdc-1(ValuationofForwardValuationofforward(Cont.)ThevalueofFRAatexpiration(t=a):' DayS)I 360 JUsesimpleinterestformoneymarketinstrument.NPx(Underlyingrate-Forwardrate)x01Underlyingrate×aDaySII360IbValuationofForwardValuationofforward(Cont.)ThevalueofFRApriortoexpiration(t<a):Step1:calculatethenewFRArate(FR)t1Sblbt1Sa：t1FRtaStep2:calculatethevalueofFRAas:NPx(FR,一FR。)(DayS既atob)j吓DaySfrOmttObj%C360J0tabPractice1TheU.S.risk-freerateis2.96%,theJapaneseyenrisk-freerateis1.00%,andthespotexchangeratebetweentheUnitedStatesandJapanis$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)=$0.00757×e(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-<一O-ra>IUnoHJ-Hog-"!ABP06IU8n。El£6IBp&JdPUe(mo-l)SBHPuo>UBGPWU-Uopuol£UoPcSBq<M-El-MraJProM0J(9×m)CO三EOTSeuo三sodMo-e001-*TdroSAeP。6ZB3=3dAnswer:B10,000,000×(5.2%-5.0%)×'JV7-136°/4935.8390/f90A15.2%×360!PricingofSwapPricingofswapPrinciple:thefixedrateinswap(FS,swaprate)shouldmakesthecontractvaluezeroatinitiation.Methodology:Areceive-floating,pay-fixedinterestrateswapisequivalenttobeinglongafloating-ratebondandshortafixed-ratebond;Ifbothbondsarepricedatpar,theinitialcashflowsarezeroandtheparpaymentsattheendoffseteachother.PVFiXedratebondPVFlOatingratebond-PdVdIUePricingandValuationofSwap
