2025年CFA《衍生品》強化練習卷考試時間：______分鐘總分：______分姓名：______一、Derivativesarefinancialinstrumentswhosevalueisderivedfromanunderlyingasset,index,orbenchmark.Whichofthefollowingstatementsbestdescribesafundamentalcharacteristicofderivativeinstruments?A)Derivativesaretypicallymarkedtomarketdaily,requiringparticipantstopostmargin.B)Theinitialcosttopurchaseaderivativecontractisgenerallyequaltothefairvalueofthederivativeatinitiation.C)Derivativesinherentlyinvolvemorecounterpartycreditriskthantheunderlyingassetstheyarebasedupon.D)Derivativesaregenerallysubjecttomoreextensiveregulatoryoversightthantheunderlyingassets.二、Aninvestorexpectsthepriceofanon-dividendpayingstocktoincreaseoverthenextsixmonths.Whichderivativestrategywouldallowtheinvestortoparticipateintheupsidepotentialofthestockwithoutrequiringthefullinitialinvestmentofpurchasingthestock?A)Sellingacalloptiononthestock.B)Buyingaputoptiononthestock.C)Buyingacalloptiononthestock.D)Enteringintoashortforwardcontractonthestock.三、TheBlack-Scholes-MertonmodelforpricingEuropeancalloptionsrequiresseveralinputs.Whichofthefollowingisakeyinputfactorthatdirectlyinfluencesthecalculatedpriceofthecalloption?A)Thedividendyieldoftheunderlyingasset.B)Thevolatilityoftheunderlyingasset'sprice.C)Theyieldonarisk-freebondwithamaturityequaltotheoption'stimetoexpiration.D)Alloftheabove.四、Atraderhasboughtacalloptionwithastrikepriceof$50andapremiumof$3.Thecurrentmarketpriceoftheunderlyingassetis$55.Whatistheintrinsicvalueoftheoption,andwhatisthetrader'scurrentprofitorloss(assumingnotimevaluehasdecayed)?A)Intrinsicvalue=$0;Profit/Loss=-$3.B)Intrinsicvalue=$3;Profit/Loss=$3.C)Intrinsicvalue=$5;Profit/Loss=$2.D)Intrinsicvalue=$5;Profit/Loss=$3.五、WhichofthefollowingstatementsregardingtherelationshipbetweenaEuropeancalloptionandaEuropeanputoption,bothwiththesamestrikeprice(K)andthesameexpirationdate(T),heldonthesameunderlyingasset,iscorrectaccordingtoput-callparity?A)Thepriceofthecalloptionmustalwaysbehigherthanthepriceoftheputoption.B)Thepriceofthecalloptionminusthepriceoftheputoptionmustequalthepresentvalueofthestrikeprice.C)Thepriceofthecalloptionplusthepriceoftheputoptionmustequalthecurrentpriceoftheunderlyingasset.D)Thepriceoftheputoptionminusthepriceofthecalloptionmustequalthepresentvalueofthestrikeprice.六、Acompanyisconcernedabouttheriskofrisinginterestratesimpactingitsfuturecashflows.Itentersintoasingle-periodinterestrateswapwhereitagreestopayafloatinginterestrate(basedonabenchmarklikeSOFR)andreceiveafixedinterestrateonanotionalprincipalamount.Whichofthefollowingbestdescribestheprimarypurposeofthisswapforthecompany?A)Tospeculateonthefuturedirectionofinterestrates.B)Tohedgeagainsttheriskofinterestratesfalling.C)Toconvertafloating-rateliabilityintoafixed-rateliability.D)Toincreaseitsexposuretointerestraterisk.七、Aportfoliomanagerhasaportfoliovaluedat$100millionwithaone-dayValueatRisk(VaR)ata99%confidencelevelof$2million.Iftheportfoliomanagerdecidestoincreasetheportfoliovalueto$120millionbyinvestinganadditional$20million,whiletheunderlyingriskfactorsremainunchanged,whatwouldbethenewone-dayVaRata99%confidencelevel,assumingtherelationshipbetweenportfoliovalueandVaRislinear?A)$2.40million.B)$2.00million.C)$1.80million.D)ThenewVaRcannotbedeterminedwithoutknowingthespecificvolatilityoftheportfolio.八、Whatistheprimarypurposeofthe"Gamma"希臘字母inoptionstrading?A)Itmeasuresthesensitivityofanoption'spricetochangesintheunderlyingasset'svolatility.B)Itmeasuresthesensitivityofanoption'sdeltatochangesintheunderlyingasset'sprice.C)Itmeasuresthesensitivityofanoption'spricetochangesintheunderlyingasset'sprice.D)Itmeasurestherateofchangeofanoption'sdeltafora$1changeintheunderlyingasset'sprice.九、Aninvestorbuysaputoptionwithastrikepriceof$45andpaysapremiumof$2.Theunderlyingassetcurrentlytradesat$40.Theinvestoralsosimultaneouslysellsaputoptionwithastrikepriceof$40andreceivesapremiumof$1.Whatistheinitialnetpremiumreceivedbytheinvestor,andwhatisthebreakevenpointforthisstrategy(assumingitisasyntheticpositionrelatedtoacall)?A)Netpremium=$1;Breakevenpoint=$39.B)Netpremium=$1;Breakevenpoint=$41.C)Netpremium=$3;Breakevenpoint=$37.D)Netpremium=$3;Breakevenpoint=$43.十、Futurescontractsaremarkedtomarketdaily.Aninvestorholdsalongpositioninafuturescontractforacommodity.Thedailysettlementpriceincreasesfrom$50to$52.Iftheinitialmarginrequirementis$2,000andthemaintenancemarginrequirementis$1,400,whatwillhappen,andwhatactionmighttheinvestorberequiredtotake?A)Nomargincall;theinvestor'saccountequityincreases.B)Amargincalloccurs;theinvestormustdepositanadditional$1,600.C)Nomargincall;theinvestor'saccountequityremainsat$2,000.D)Amargincalloccurs;theinvestormustdepositanadditional$1,200.十一、Acompanyneedstopay€10millionin6months.TohedgeagainstpotentialadversemovementsintheEUR/USDexchangerate,itentersintoacurrencyforwardcontracttosell€10millionandbuyUSD.Thecurrentforwardexchangerateis1.10USD/EUR.Ifthe6-monthforwardpointshaveincreasedby50basispointsduetochangesininterestratedifferentialsbetweentheUSandtheEurozone,whatisthenewforwardexchangeratethecompanywilleffectivelylockin?A)1.0750USD/EUR.B)1.1000USD/EUR.C)1.1250USD/EUR.D)1.1500USD/EUR.十二、Whichofthefollowingstatementsaboutthe"Vega"希臘字母ofanoptionismostaccurate?A)Itmeasuresthesensitivityoftheoption'sdeltatochangesintheunderlyingasset'sprice.B)Itmeasuresthesensitivityoftheoption'sgammatochangesintheunderlyingasset'sprice.C)Itmeasuresthesensitivityoftheoption'spricetochangesinthevolatilityoftheunderlyingasset.D)Itrepresentsthemaximumpossiblechangeintheoption'spriceifthevolatilityweretoincreaseby1%.十三、Consideraswaptionthatgivestheholdertheright,butnottheobligation,toenterintoaninterestrateswapinthefuture.Whichofthefollowingstatementscorrectlydescribesapotentialpayoffstructureforthisswaptionatexpiration?A)Thepayoffislinearlyrelatedtothedifferencebetweenthefixedandfloatingswapratesiftheswaptionisexercisedandtheswapisinitiatedatmarketrates.B)Thepayoffiszeroiftheswaptionisnotexercised.C)Thepayoffisbasedsolelyonwhethertheunderlyingforwardinterestrateisaboveorbelowapredeterminedstrikerateattheswaption'sexpirationdate.D)Thepayoffisdeterminedbythenotionalamountandthedurationoftheswap,regardlessoftheswaprates.十四、Atradersells(writes)aputoptionwithastrikepriceof$25andreceivesapremiumof$4.Theunderlyingassetpriceatexpirationis$28.Whatisthetrader'sprofitorlossonthisoptionposition?A)Profit=$4.B)Profit=$24.C)Loss=$4.D)Loss=$21.十五、Theriskofadversepricemovementsinaderivativecontractnotresultingfromthepricemovementoftheunderlyingassetisknownas:A)Basisrisk.B)Cross-hedgerisk.C)Deltarisk.D)Contangorisk.十六、Aninvestorbuysacalloptionandsimultaneouslysellsaputoption,bothwiththesamestrikeprice(K)andthesameexpirationdate(T),onthesameunderlyingasset.Whichofthefollowingstatementsbestdescribesthisstrategy?A)Itisabullishstrategywithunlimitedpotentialprofitandlimitedrisk.B)Itisaneutralstrategywithlimitedpotentialprofitandrisk.C)Itisabullishstrategywithlimitedpotentialprofitandrisk.D)Itisaprotectivestrategydesignedtolimitdownsiderisk.十七、AswapdealerentersintoacurrencyswaptoconvertUSDcashflowsintoEURcashflowsforaclient.Thedealeritselfiseffectively:A)ExposedtointerestrateriskontheUSDsideandEURsideoftheswap.B)Transferringthecounterpartycreditriskoftheclienttothemarket.C)Actingasanintermediary,takingontheoppositesideofthecurrencyexposurefortheclient.D)Hedgingitsownforeignexchangeriskresultingfromotherclienttransactions.十八、WhenusinghistoricalsimulationtoestimateValueatRisk(VaR),whichofthefollowingassumptionsisimplicitlymade?A)Futureportfolioreturnswillbenormallydistributed.B)Thestatisticalpropertiesofpastreturnsareexpectedtopersistintothefuture.C)Thelargestlossobservedinthehistoricalperiodwillbethemaximumlosspossible.D)Thecorrelationbetweendifferentassetsintheportfoliowillremainconstant.十九、Whichofthefollowingstatementsabouttherelationshipbetweenafuturespriceandthespotpriceoftheunderlyingassetisgenerallytruefornon-dividendpayingassets?A)Thefuturespriceisalwaysequaltothespotprice.B)Thefuturespriceisalwayshigherthanthespotprice(contango).C)Thefuturespriceisalwayslowerthanthespotprice(backwardation).D)Thefuturespricecanbehigherorlowerthanthespotpricedependingonmarketexpectationsandtimetomaturity.二十、AninvestorbuysacalloptiononStockAandaputoptiononStockB.Ifbothoptionshavethesamestrikeprice(K)andthesameexpirationdate(T),andthecurrentpricesofStockAandStockBarePAandPBrespectively,thevalueofthisportfoliocanbeexpressedas:A)Max(PA-K,0)+Max(PB-K,0).B)Max(PA+PB-2K,0).C)Max(K-PA,0)+Max(K-PB,0).D)PA-PB.試卷答案一、A解析：選項A描述了衍生品（尤其是期貨）通常的每日盯市制度（MarkedtoMarket）和保證金要求（Margin），這是其區(qū)別于普通股票或債券的一個顯著特征。選項B錯誤，購買衍生品（尤其是期權(quán)）的初始成本通常遠低于其潛在價值，因為購買的是未來價值變動的權(quán)利。選項C錯誤，衍生品如果未進行對沖，可能比underlyingassets涉及更高的counterpartycreditrisk。選項D錯誤，監(jiān)管程度取決于具體品種和司法管轄區(qū)，并非普遍規(guī)律。二、C解析：購買看漲期權(quán)（Buyingacalloption）允許投資者以固定的行權(quán)價購買股票，從而在股價上漲時獲得收益，而無需像直接購買股票那樣支付全部股價。這符合題干描述的“以較低成本參與上漲潛力”。選項A賣出看漲期權(quán)是投機或?qū)_策略，風險方向與投資者預(yù)期相反。選項B買入看跌期權(quán)是投機于股價下跌。選項D做空期貨是押注股價下跌，且需要繳納初始保證金。三、D解析：Black-Scholes-Merton模型的核心輸入包括：標的資產(chǎn)當前價格、行權(quán)價格、無風險利率、模型期限（到期日）、標的資產(chǎn)連續(xù)復利股息率（對于不支付股息的資產(chǎn)為0）、標的資產(chǎn)價格波動率。其中，無風險利率是計算現(xiàn)值（如行權(quán)價格的現(xiàn)值）的關(guān)鍵輸入，波動率是衡量價格不確定性，直接影響期權(quán)時間價值的輸入。選項A（股息率）在非股息支付資產(chǎn)中為0，但在股息支付資產(chǎn)中是重要輸入。選項B（波動率）是模型中唯一非觀測輸入，對期權(quán)價格影響巨大。選項C（無風險利率）雖然重要，但不如波動率那樣直接影響價格的計算本身，波動率的不確定性是期權(quán)價值的核心來源。四、C解析：期權(quán)內(nèi)在價值（IntrinsicValue）=Max(標的資產(chǎn)價格-行權(quán)價格,0)。本題中，內(nèi)在價值=Max($55-$50,0)=$5。交易者買入期權(quán)支付了$3的溢價，當前利潤/損失=內(nèi)在價值-溢價=$5-$3=$2（利潤）。因此，選項C正確。選項A內(nèi)在價值為0，利潤為-$3（損失等于支付的費用）。選項B內(nèi)在價值為$3，利潤為$3。選項D內(nèi)在價值為$5，利潤為$3。五、C解析：根據(jù)歐式看跌期權(quán)-看漲期權(quán)平價定理（Put-CallParityforEuropeanoptions）：C+P=S0-Ke^(-rT)。其中C是看漲期權(quán)價格，P是看跌期權(quán)價格，S0是標的資產(chǎn)當前價格，K是行權(quán)價格，r是無風險利率，T是到期時間。該公式可以變形為：C-P=S0-Ke^(-rT)。因此，看漲期權(quán)價格減去看跌期權(quán)價格等于標的資產(chǎn)現(xiàn)價減去行權(quán)價格的現(xiàn)值。選項A、B、D均不符合平價關(guān)系公式。六、C解析：公司通過支付浮動利率、收取固定利率的互換，將未來的浮動利率負債（如貸款）轉(zhuǎn)換為固定利率負債。這樣做的主要目的是對沖利率上升的風險，鎖定未來的利息支出。選項A錯誤，此為對沖行為而非投機。選項B錯誤，策略是為了對沖利率上升。選項D錯誤，公司是希望減少而非增加利率風險暴露。七、A解析：根據(jù)線性關(guān)系假設(shè)，VaR與投資組合規(guī)模成正比。VaR=PortfolioValue*VaRRatio。原VaRRatio=$2M/$100M=0.02。新投資組合規(guī)模為$120M，新VaR=$120M*0.02=$2.40M。選項B是原VaR值。選項C錯誤，VaR隨規(guī)模增加而增加。選項D錯誤，雖然需要知道波動率才能精確計算，但題目假設(shè)線性關(guān)系，且給出了比例。八、B解析：Gamma（Γ）衡量的是期權(quán)Delta值對于標的資產(chǎn)價格變化的敏感度，即Delta值的變化率。Delta本身衡量的是期權(quán)價格對于標的資產(chǎn)價格變化的敏感度。Vega衡量的是期權(quán)價格對波動率變化的敏感度。因此，Gamma是Delta的Delta，衡量Delta的變化速度。九、D解析：該策略是買入執(zhí)行價較高的看跌期權(quán)（P45）并賣出執(zhí)行價較低的看跌期權(quán)（P40），形成寬跨式看跌期權(quán)（BroadStraddle）。初始凈溢價=收到的溢價-支付的溢價=$1-$2=-$1（凈支付費用）。該策略的盈虧平衡點在兩個執(zhí)行價之間，具體為：盈虧平衡點=較高行權(quán)價+凈支付費用=$45+(-$1)=$44。但題目問的是與合成看漲相關(guān)的盈虧平衡點，此策略是賣出看跌合成看漲（ShortPut,LongCall）。對于合成看漲，盈虧平衡點=較低行權(quán)價-凈支付費用=$40-(-$1)=$41。因此，選項D正確。注意：此策略初始凈成本為-1，盈虧平衡點為41。十、B解析：每日結(jié)算價從$50增加到$52，價差增加$2。初始保證金為$2,000，維持保證金為$1,400。維持保證金是初始保證金的70%($1,400/$2,000=0.7)。賬戶權(quán)益變化=$2*(52-50)=$4。新賬戶權(quán)益=$2,000+$4=$2,004。新的保證金比率=$2,004/(新結(jié)算價*合約乘數(shù))=$2,004/($52*X)，其中X是合約乘數(shù)（題目未給，但在計算中會被約掉）。假設(shè)合約乘數(shù)為1，新保證金比率=$2,004/$52≈0.385。原保證金比率=$2,000/$50=0.4。新比率低于原比率，但高于維持保證金比率（0.7）。如果題目假設(shè)合約乘數(shù)為100，則新比率=$2,004/($52*100)≈0.0385，遠低于維持保證金比率，會發(fā)生MarginCall。由于選項中只有$1,600的追加要求，且新權(quán)益$2,004遠高于$1,400，且高于$2,000，因此嚴格來說不會觸發(fā)MarginCall。但選項設(shè)置可能基于不同假設(shè)或簡化，最接近的情況是初始權(quán)益增加，不會觸發(fā)追加。重新審視，新權(quán)益$2,004>初始$2,000，大于維持$1,400，沒有低于維持水平。選項B（追加$1,600）是不可能的。選項A（無追加，權(quán)益增加）最符合計算結(jié)果。此題選項設(shè)置可能存在問題或假設(shè)不清?；跇藴势谪浻嬎?，新權(quán)益$2,004>$2,000>$1,400，無MarginCall。如果必須選一個最接近“可能發(fā)生追加”的，可能題目想表達的是如果前一天結(jié)算價為$48，則新結(jié)算$50，權(quán)益$2,000+$4=$2,004>$1,400，無追加?；蛘哳}目假設(shè)了更高的合約乘數(shù)導致新權(quán)益低于維持水平。按最直接計算，無追加。假設(shè)題目意在考察MarginCall機制，需要新權(quán)益低于維持水平。重新審視，$2,004>$1,400，無MarginCall。題目選項可能錯誤。若按標準計算，答案應(yīng)為A。但題目要求必須選擇一個?？赡茉谔囟ㄇ榫诚拢ㄈ绺叱藬?shù)或不同維持比）會觸發(fā)。按最簡單情況（乘數(shù)1），不觸發(fā)。選擇A。十一、C解析：原前向匯率是1.10USD/EUR。6個月前向點增加50基點（bps）意味著現(xiàn)在需要支付更多的USD來購買1EUR，或者用1EUR可以換到更多的USD。增加50bps相當于增加了0.0050。新前向匯率=1.10+0.0050=1.1050USD/EUR。十二、C解析：Vega（ν）衡量的是期權(quán)價格對于標的資產(chǎn)波動率（Volatility）變化的敏感度。波動率越高，期權(quán)的時間價值通常越高，因為更大的波動性意味著更大的潛在價格變動可能性。選項A是Vega的定義。選項B是Gamma的定義。選項D描述的是Vega衡量影響，但不是其定義。十三、B解析：對于未行使的期權(quán)，其價值在到期時為零。如果期權(quán)的價值在到期時為正（即被行使），則持有者會行使期權(quán)，獲得正的現(xiàn)金流。如果期權(quán)的價值在到期時為負或零，持有者不會行使，因為會損失錢。因此，如果swaption未被行使，其價值為零。十四、A解析：賣出（寫）看跌期權(quán)（PutOption）收取溢價$4。如果到期時標的資產(chǎn)價格（$28）高于行權(quán)價（$25），則看跌期權(quán)不會被行使，賣方賺取全部溢價$4。因此，利潤等于收到的溢價$4。十五、B解析：Cross-hedgerisk（交叉對沖風險）是指使用一種衍生品對沖另一種（通常不直接相關(guān)）風險exposures時，由于對沖工具與被對沖風險之間的不完全相關(guān)性而產(chǎn)生的風險?；铒L險（Basisrisk）是指期貨價格與現(xiàn)貨價格之間關(guān)系（基差）的不確定性導致的風險，雖然也涉及價格關(guān)系，但Cross-hedg