CFA二級(jí)基礎(chǔ)班-衍生-標(biāo)準(zhǔn)版

CFA二級(jí)培訓(xùn)項(xiàng)目

講師：TOM

m魚藝櫛MM6aPr中血嗎

TopicWeightingsinCFALevelII

SessionNO.ContentWeightings

StudySession1Ethical&ProfessionalStandards10-15

StudySession2-3QuantitativeMethods5-10

StudySession4Economics5-10

StudySession5-6FinancialReportingandAnalysis10-15

StudySession7-8CorporateFinance5-10

StudySession9-11Equity10-15

StudySession12-13FixedIncome10-15

StudySession14Derivatives5-10

StudySession15AlternativeInvestments5-10

StudySession16-17PortfolioManagement10-15

行業(yè)?創(chuàng)新?憎值

(S)FrameworkSS14Derivatives

?R37PricingandValuationof

ForwardCommitments

Derivatives?R38ValuationofContingent

Claims

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PricingandValuationofForwardCommitments

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行業(yè)?創(chuàng)新?憎值

1.Forward

■PrincipleofArbitrage-freePricing

Framework■EquityForwardandFuturesContracts

■InterestRateForwardandFutures

Contracts(FRA)

■Fixed-IncomeForwardandFuturesContracts

■CurrencyForwardContracts

2.T-bondFutures

3.Swap

■InterestRateSwapContracts

■CurrencySwapContracts

■EquitySw叩Contracts

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專業(yè)?創(chuàng)新?憎值

?ForwardContracts

“Aforwardcontractisanagreementbetweentwopartiesinwhichone

party,thebuyer,agreestobuyfromtheotherparty,theseller;anunderlying

assetorotherderivative,atafuturedateatapriceestablishedatthestartof

thecontract.最新資料領(lǐng)取微信xiiebajun888s

“Longposition:apositioninanassetorcontractinwhichoneownstheasset

orhasanexercisablerightunderthecontract.

jShortposition:apositioninanassetorcontractinwhichonehassoldan

assetordoesnotown,orinwhicharightunderacontractcanbeexercised

againstoneself.

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PriceandValue

Thepriceisthepredeterminedpriceinthecontractthatthelongshould

paytotheshorttobuytheunderlyingassetatthesettlementdate.

Thecontractvalueiszerotobothpartiesatinitiation.

Theno-arbitrageprinciple:tradablesecuritieswithidenticalcashflow

paymentsmusthavethesameprice.Otherwise,traderswouldbeableto

generaterisk-freearbitrageprofits.

?Twoassetsorportfolioswithidenticalfuturecashflows,regardlessof

futureevents,shouldhavesameprice;

?Theportfolioshouldyieldtherisk-freerateofreturn,ifitgenerates

certainpayoffs.

T

?Generalformula:FP=S0X(l+Rf)

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?ForwardsArbitrage

>Cash?and?CarryArbitragewithforwardcontractmarketpriceto。high

relativetocarryarbitragemodel.

?IfFP>S0X(1+Rff

AtinitiationAtsettlementdate

?Shortaforwardcontract?Delivertheunderlyingtothelong

?BorrowSoattherisk-free?GetFPfromthelong

rate?Repaytheloanamountof

?UsethemoneytobuytheSoX(l+Rf)T

underlyingbond

Profit=FP-S0X(l+Rf)T

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?ForwardsArbitrage

>ReverseCasivsnd-CarryArbitragewithforwardcontractmarketpriceto。

lowrelativetocarryarbitragemodel.

?IfFP<S0X(l+Rff

AtinitiationAtsettlementdate

?Longaforwardcontract?PaytheshortFPtogetthe

underlyingbond

?Shortselltheunderlying

?Closeouttheshortpositionby

bondtogetSodeliveringthebond

?InvestSoattherisk-freerate?Receiveinvestmentproceeds

S0X(URf)T

Profit=S°X(l+Rf)「FP

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?GenericPricing:No-ArbitragePrinciple

>Pricingaforwardcontractistheprocessofdeterminingtheno-arbitrage

pricethatwillmakethevalueofthecontractbezerotobothsidesatthe

initiationofthecontract.

?Forwardprice=pricethatwouldnotpermitprofitablerisklessarbitrage

infrictionlessmarkets

?)

FP=Sox(l+rfT+CarryingCosts-CarryingBenefits

>Va山ationofaforwardcontractmeansdeterminingthevalueofthe

contracttothelong(ortheshort)atsometimeduringthelifeofthe

contract.

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行業(yè)?創(chuàng)新?憎值

Forwardcontractvalue

T-bill(zero-couponbond)forwards

?buyaT-billtodayatthespotprice(So)andshortaT-monthT-bill

forwardcontractattheforwardprice(FP);

-x(l趣.

理)------

?Forwardvalueoflongpositionatinitiation(t=0)zduringthecontract

life(t=t)zandatexpiration(t=T).

TimeForwardContractValuation

Zero,becausethecontractispricedtoprevent

t=0arbitrage

t=t

芟（1+

B、理一淺

或

t=T明

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專業(yè)?創(chuàng)新?憎值

?EquityForwardContracts

>Forwardcontractsonadividend-payingstock

?Price:理瑕=6母一瑞fl演）x（爭(zhēng)羊

百）./

?Value:品在斫冕-啜真＞（1+7—

袋■糧更）.桂

「到/圜釗、函慧型一。卷）

圖=伙,M哦矍一0可）用吟￥1、一一技

=+晉q

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行業(yè)?創(chuàng)新?憎值

?Example

圜>Assumingaforwardcontractwith100daysuntilmaturityonastock,

thestockpriceis$45andexpectedtopaydividendof$0.3in20days,

and$0.5in75days.Theriskfreerateis4%.Calculatetheno-arbitrage

forwardprice.

>CorrectAnswer:

So=$45

Di=$0.3D2=$0.5FP=?

I▲IAk

02075100days

$0.3,$0.5

10420/365+10475/365$0.795343

旬果=($45-$0,795343)x1.O4100/365=$44,68

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?Example

圜>After40days,thestockpricechangedto$48.Calculatethevaluationof

theforwardcontract.

>CorrectAnswer:

?There'sonlyonedividendremaining(in35days)beforethe

contractmatures(in60days)asshownbelow；so:

So=$45Di=$0,3S40二$48D=$0.5FP=$44.68

I2

2040y75100days

35daysJ

x，_60days

—o

$0.5

]0435/365=$0.498123

契40$44.68

田。（碧衽哥強(qiáng)吾衽莖=($48—]0460/365=$3,11

$0.498123）-

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行業(yè)?創(chuàng)新?憎值

?Example

>Onemonthago,Todpurchasedaforwardcontractwiththreemonths

toexpirationataquotedpriceof100.20(quotedasaper100par

Bvalue).Thecontractnotionalamountis￥100,000,000.Thecurrent

forwardpriceis100.05.Theriskfreerateis0.3%.Thevalueofthe

positionisclosestto:

A.-￥149,925.

B.-￥150,000.

C.-￥150,075.

“CorrectAnswer:A.最新資料領(lǐng)取微信xuebajun888s

?ThevalueofTod'sforwardpositioniscalculatedas

馥翌=母葭到名(一)]

咫碧

黑(里專100.05-100^0(/1+產(chǎn)12=-0.149925(吾強(qiáng)蕓100年利表

0.0030普器理法很)

?Therefore,thevalueoftheTod'sforwardpositionis

r「0.149925

留《毛—(￥100,000,000)=-￥149,925

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專業(yè)?創(chuàng)新?憎值

?EquityIndexForwardContracts

>Forwardcontractsonanequityindex

c-In1+Kf

?Continuouslycompoundedrisk-freerate:Rf^^

?Continuouslycompoundeddividendyield:6C

?Price:即裝=圖0避

?Value：誓鏟(jpM)一(點(diǎn)心)

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行業(yè)?創(chuàng)新?憎值

?Example

圜>AssumingaforwardcontractontheDowJonesIndexwith100days.

Currently,thevalueofDowJonesIndexis21,000andthecontinuous

dividendyieldis2%.Thecontinuouslycompoundedriskfreerateis

3.2%.Calculatetheno-arbitragepriceoftheforwardcontract.

)

FP=21,000X^(0.032-0.02)x(100/365=21069.1547

>After75days,thevalueofDowJonesIndexis20,050.Keeptherisk

freerateanddividendyieldsameasbefore.Calculatethevaluationof

theforwardcontract.

20,05021,069.1547

Vr(longposition)=------強(qiáng)?亡-一~強(qiáng)c=-1,000.481

7畜0.02x(25/365)<10.032x(25/365)

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?ForwardContractsonCouponBonds

>Couponbonds

?Similartodividend-payingstocks,butthecashflowsarecoupons

?Price:利果=金一福留裸）x@嗎

+?)

?Value:矗衽鏟（春演一7TTT--------

艱氯等】鞅技）一%決）蛋.我

用段胤豆干敢割罡嚏）汜Z田

留的理］

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?Example

圜>Assumingaforwardcontractwith150daysonaUStreasurybill.The

UStreasurybillhasa5%couponrate,thepriceis$1,100andwillmake

couponpaymentin90days.Theriskfreerateis4%.Calculatethe

forwardprice.

>CorrectAnswer:

”$1000x0.05

段=-----z--------=$25

—】$25.00

營利段01.049。/365=$2生7594

?Theforwardpriceofthecontractistherefore:

旬累(onaincuniesecurity)=($1,100—S24.7594)x

1.04150/365=1,092.7122.

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?CurrencyForwardContracts

Price:coveredInterestRateParity(IRP)

一］(1+雪奧)

理歆=若。(1+-2沼

x

FPandSoarequotedincurrencyDperunitofcurrencyF(i.e.fD/F)

Value:

斗.

己1-

（1+整金尸-丁一^:

用決）-一

Ifyouaregiventhecontinuousinterestrates

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?Example

圜>Considerthefollowing:TheU.S.risk-freerateis6percent,theSwiss

risk-freerateis4percent,andthespotexchangeratebetweenthe

UnitedStatesandSwitzerlandis$0.6667.

?CalculatethecontinuouslycompoundedU.S.andSwissrisk-free

rates;

?Calculatethepriceatwhichyoucouldenterintoaforwardcontract

thatexpiresin90days;

?Calculatethevalueoftheforwardposition25daysintothe

contract.Assumethatthespotrateis$0.65.

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?CurrencyForwardContracts

>CorrectAnswer:

1.rCHF=ln(1.04)=0.0392;r$=ln(1.06)=0.0583

2

.閱玨g.666腔各9爆曬392("U/36b))⑶o.o583(W/36b))=

$0.6698

3.St=$0.65;T=90/365;t=25/365;T-t=65/365

Thevalueofthecontractis-$0.0174perSwissfranc

第t(0,T)=($0.65x毀一。。392(65/365))_($06698x

程-0.0583(6勺/365))

=-$0.0174

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行業(yè)?創(chuàng)新?憎值

?ForwardRateAgreements(FRAs)

>AForwardRateAgreement(FRA)isaforwardcontractonaninterest

rate(LIBOR).

■Thelongpositioncanbeviewedastherightandtheobligationto

borrowattheforwardrateiathefuture;

?Theshortpositioncanbeviewedastherightandtheobligationtolend

attheforwardrateinthefuture;

?Noloanisactuallymade,andFRAsarealwayssettledincashatcontract

expiration.

>Let'stakea1X4FRAforexample.A1X4FRAis

?aforwardcontractexpiresin1month,

?andtheunderlyingloanissettledin4months,

?witha3-monthnotionalloanperiod.

?Theunderlyinginterestrateis90-dayLIBORin30daysfromnow.

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?ForwardRateAgreements(FRAs)

>LIBOR(LondonInterbankOfferedRate):Collectivenameformultiple

ratesatwhichaselectsetofbanksbelievetheycouldborrowunsecured

fundsfromotherbneksintheLondoninterbankmarketfordifferent

currenciesanddifferentborrowingperiodsrangingfromovernighttoone

year.

?anannualizedratebasedona360-dayyear

?anadd-onrate

?thereferencerateformanyfloating-ratebonds

?USDinterestrate

?publisheddailybytheBritishBanker'sAssociation

>Euribor(EuropeInterbankOfferedRate):establishedinFrankfurt,and

publishedbyEuropeanCentralBank.

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?ForwardPricingandValuation-FRA

>LIBOR,Euribor,andFRAs(Con't)

Settlement:settleincash,butnoactualloanismadeatthesettlementdate.

?Payoffqualitativeanalysis:

/Ifthereferencerateattheexpirationdateisabovethespecified

contractrate,thelongwillreceivecashpaymentfromtheshort;

/Ifthereferencerateattheexpirationdateisbelowthecontractrate,

theshortwillreceivecashpaymentfromthelong.

?Payoffquantitativeanalysis

days

(Floatingrateatsettlement-forwardrate)

(Notionalprincipal)

1+Floatingrateatsettlement

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行業(yè)?創(chuàng)新?憎值

?Example

圜>In30days,aUKcompanyexpectstomakeabankdepositof

￡10,000,000foraperiodof90daysat90-dayLiborset30daysfrom

today.Thecompanyisconcernedaboutapossibledecreaseininterest

rates.Thecompanyentersintoa￡10,000,000notionalamount1X4

receive-fixedFRA.TheappropriatediscountrrtcfortheFRAsettlement

cashflowsis0.40%.After30days,90-dayLiborinBritishpoundsis

0.55%.最新資料領(lǐng)取微信xuebajun888s

IftheFRAwasinitiallypricedat0.60%,thepaymentreceivedtosettleit

willbeclosestto:

A.-￡2,448.75.

B.￡1,248.75.

C.￡1,250.00.

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行業(yè)?創(chuàng)新?憎值

?Example

昌j>CorrectAnswer:B.

?Thesettlementamountofthe1X4FRAathforreceive-fixedis

?NA{[FRA(0hm)-Lh(m)]tm}/[1+Dh(m)tm]

二[10,000,000(0.0060-0.0055)(0.25)]/[l+0.0040(0.25)]

=￡1,248.75.

?BecausetheFRAinvolvespayingfloating,itsvaluebenefitedfroma

declineinrates.

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?FRAPricing

>TheforwardpriceinanFRAistheno-arbitrageforwardrate(FR)

?Ifspotratesareknown,TheFRisjusttheunbiasedestimateofthe

forwardinterestrate:

-------?L(m)/m-------1-------?FR/n------

--------------?L(m+n)/m+n?----------------

(1+堂理x鎏/360)(1+理mx噂/360)=(1+琛加嗯x(翌+

善)/360)

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行業(yè)?創(chuàng)新?憎值

?Example

>Calculatethepriceofa1X4FRA.Thecurrent30-dayLIBORis3%and

120-dayLIBORis3.9%.

>CorrectAnswer:

(1+3%x30/360)[1+FRAox(120-30)/360]=(1+3.9%x120/360)

?TheannualizedforwardrateisFRAo=4.2%.

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行業(yè)?創(chuàng)新?憎值

?Example

圜>Supposeweenteredareceive-floating6X9FRAatarateof0.86%,

withnotionalamountofC$10,000,000atTime0.Thesix-monthspot

Canadiandollar(C$)Liborwas0.628%,andthenine-monthC$Libor

was0.712%.After90dayshavepassed,thethree-monthC$Liboris

1.25%andthesix-monthC$Liboris1.35%.

AssumingtheappropriatediscountrateisC$Libor,thevalueofthe

originalreceive-floating6X9FRAwillbeclosestto:

A,C$14,125.

B.C$14,350.

C.C$14,651.

30-148

行業(yè)?創(chuàng)新?憎值

?Example

>CorrectAnswer:C.

?First,calculatethequotedFRAatt=90

(1+1.25%x90/360)[1+FRA90x(180-90)/3601(1+1.35%x180/360)

/TheannualizedforwardrateisFRA90=1.4455%.

?Second,calculatethevalueofFRAatt=90

ViOng=10z000z000[(0.014455-0.0086)(90/360)]/[l+0.0135(180/360)]

=14,539.35

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行業(yè)?創(chuàng)新?憎值

1.Forward

■PrincipleofArbitrage-freePricing

Framework■EquityForwardandFuturesContracts

■InterestRateForwardandFutures

Contracts(FRA)

■Fixed-IncomeForwardandFuturesContracts

■CurrencyForwardContracts

2.T-bondFutures

3.Swap

■InterestRateSwapContracts

■CurrencySwapContracts

■EquitySw叩Contracts

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專業(yè)?創(chuàng)新?憎值

FuturesContractValue

Thevalueofafuturescontractiszeroatcontractinception.

Futurescontractsaremarkedtomarketdaily,thevaluejustaftermarking

tomarketisresettozero.

Betweenthetimesatwhichthecontractismarkedtomarket,thevaluecan

becHfferentfromzero.

?V(long)=currentfuturesprice-futurespriceatthelastmark-to-

markettime.

Anotherviewoffutures:settlepreviousfutures,andthenopenanother

newfutureswithsamedateofmaturity.

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行業(yè)?創(chuàng)新?憎值

T-bondFuturesContracts

Underlying:Hypothetical30yeartreasurybondwith6%couponrate.

Bondcanbedeliverable:$100,000parvalueT-bondswithanycouponbut

withamaturityofatleast15years.

Thequotesareinpointsand32nds:Apricequoteof95-18isequalto

95.5625andadollarquoteof$95,562.50.

Theshorthasadeliveryoptiontochoosewhichbondtodeliver.Eachbond

isgivenaconversionfactor(CF),whichmeansaspecificbondis

equivalenttoCFstandardbondunderlyinginfuturescontract.

?ForaspecificBondA:

現(xiàn)毀標(biāo)準(zhǔn)=即數(shù)咽￡—

X歆噌

Theshortdesignateswhichbondhewilldriver(cheapest-to-deliverbond).

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行業(yè)?創(chuàng)新?憎值

?ArbitragefromT-Bondfutures

>TherearemethodstobuytheunderlyingbondA

?BuybondAthroughT-bondfutures

/Theadjustedpriceofthefuturescontractisequaltotheconversion

factormultipliedbythequotedfuturesprice:

理零理=即歌根sx?現(xiàn)

/AddingtheaccruedinterestofAhatexpiration,theadjustedprice

ofthefuturescontractgivesatotalpriceof:

第1=現(xiàn)嗷標(biāo)準(zhǔn)x型現(xiàn)理+

制理理

?Buybondthroughholdingthebondatthebeginningoftheperiod

/theno-arbitragefuturespriceatexpirationisequaltothefollowing:

組-$京22檔）“（1也建）—

>Theavailablearbitrage而扁1is補(bǔ)金presentvalueofthisdifference

噌裝型i技裝/勇哥旁晴笠迎i卷|

=致留型2—留

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行業(yè)?創(chuàng)新?憎值

?Example-Arbitrage

>Troubadouridentifiesanarbitrageopportunityrelatingtoafixed-

圜incomefuturescontractanditsunderlyingbond.Currentdataonthe

futurescontractandunderlyingbondarepresentedinExhibit.The

currentannualcompoundedrisk-freerateis0.30%.

Exhibit1CurrentDataforFuturesandUnderlyingBond

FuturesContractUnderlyingBond

Quotedfuturesprice125.00Quotedbondprice112.00

Conversionfactor0.90Accruedinterestsincelastcoupon0.08

payment

TimeremainingtocontractexpirationThreeAccruedinterestatfuturescontract0.20

monthsexpiration

Accruedinterestoverlifeoffutures0.00

contract

BasedonExhibitandassumingannualcompounding,thearbitrage

profitonthebondfuturescontractisclosestto:

A.0.4158.

B.0.5356.

C.0.6195.

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行業(yè)?創(chuàng)新?憎值

?Example

圜>CorrectAnswer:B.

Therearemethodstobuytheunderlyingbond:

?BuybondthroughT-bondfutures

/Theadjustedpriceofthefuturescontractisequaltothe

conversionfactormultipliedbythequotedfuturesprice:

F0(T)=CF(T)QF0(T)=(0.90)(125)=112.50

/Addingtheaccruedinterestof0.20atexpiration,theadjusted

priceofthefuturescontractgivesatotalpriceof112.70.

?Buybondthroughholdingthebondatthebeginningoftheperiod

/theno-arbitragefuturespriceatexpirationisequaltothe

following:用(矍=他制)］聿明+■虱目

=(1(112.00+0.08-0)=112.1640

?Theavailablearbitrageprofitisthepresentvalueofthis

difference:(112.70-112.1640)/(1.003)0.25=0.5356.

37-148

行業(yè)?創(chuàng)新?憎值

?Quotedfuturespriceandforwardprice

>Thequotedfuturespriceisadjustedwithconversionfactor

現(xiàn)利果招歆=（=+嘲^x（i^）—理者-］。

學(xué)朝母祖思黑刑者救X之

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行業(yè)?創(chuàng)新?憎值

?Example

圜>Euro-bondfutureshaveacontractvalueof€100,000,andthe

underlyingconsistsoflong-termGermandebtinstrumentswith8.5to

10.5yearstomaturity.TheyaretradedontheEurex.Supposethe

underlying2%Germanbondisquotedat€108andhasaccrued

interestof€0.083(one-halfofamonthsincelastcouponwhichpays

annually).Theeuro-bondfuturescontractmaturesinonemonth.At

contractexpiration,theunderlyingbondwillhaveaccruedinterestof

€0.25,therearenocouponpaymentsdueuntilafterthefutures

contractexpires,andthecurrentone-monthrisk-freerateis0.1%,The

conversionfactoris0.729535.Theequilibriumeuro-bondfuturesprice

basedonthecarryarbitragemodelwillbeclosestto:

A.€147.57.

B.€147.82.

C.€148.15.

39-148

行業(yè)?創(chuàng)新?憎值

?Example

>CorrectAnswer:B.

Inthiscase,wehaveT=1/12,CF(T)=0.729535,B0(T+Y)=108z

FVCI0J=0,AI0=0.5(2/12)=€0.083,AIT=1.5(2/12)=0.25,r=0.1%.

QF0(T)=[1/CF(T)]{FVOJ[BO(T+Y