2025年CFA《衍生品》强化练习卷

2025年CFA《衍生品》强化练习卷考试时间：______分钟总分：______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"希腊字母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"希腊字母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.试卷答案一、A解析：选项A描述了衍生品（尤其是期货）通常的每日盯市制度（MarkedtoMarket）和保证金要求（Margin），这是其区别于普通股票或债券的一个显著特征。选项B错误，购买衍生品（尤其是期权）的初始成本通常远低于其潜在价值，因为购买的是未来价值变动的权利。选项C错误，衍生品如果未进行对冲，可能比underlyingassets涉及更高的counterpartycreditrisk。选项D错误，监管程度取决于具体品种和司法管辖区，并非普遍规律。二、C解析：购买看涨期权（Buyingacalloption）允许投资者以固定的行权价购买股票，从而在股价上涨时获得收益，而无需像直接购买股票那样支付全部股价。这符合题干描述的“以较低成本参与上涨潜力”。选项A卖出看涨期权是投机或对冲策略，风险方向与投资者预期相反。选项B买入看跌期权是投机于股价下跌。选项D做空期货是押注股价下跌，且需要缴纳初始保证金。三、D解析：Black-Scholes-Merton模型的核心输入包括：标的资产当前价格、行权价格、无风险利率、模型期限（到期日）、标的资产连续复利股息率（对于不支付股息的资产为0）、标的资产价格波动率。其中，无风险利率是计算现值（如行权价格的现值）的关键输入，波动率是衡量价格不确定性，直接影响期权时间价值的输入。选项A（股息率）在非股息支付资产中为0，但在股息支付资产中是重要输入。选项B（波动率）是模型中唯一非观测输入，对期权价格影响巨大。选项C（无风险利率）虽然重要，但不如波动率那样直接影响价格的计算本身，波动率的不确定性是期权价值的核心来源。四、C解析：期权内在价值（IntrinsicValue）=Max(标的资产价格-行权价格,0)。本题中，内在价值=Max($55-$50,0)=$5。交易者买入期权支付了$3的溢价，当前利润/损失=内在价值-溢价=$5-$3=$2（利润）。因此，选项C正确。选项A内在价值为0，利润为-$3（损失等于支付的费用）。选项B内在价值为$3，利润为$3。选项D内在价值为$5，利润为$3。五、C解析：根据欧式看跌期权-看涨期权平价定理（Put-CallParityforEuropeanoptions）：C+P=S0-Ke^(-rT)。其中C是看涨期权价格，P是看跌期权价格，S0是标的资产当前价格，K是行权价格，r是无风险利率，T是到期时间。该公式可以变形为：C-P=S0-Ke^(-rT)。因此，看涨期权价格减去看跌期权价格等于标的资产现价减去行权价格的现值。选项A、B、D均不符合平价关系公式。六、C解析：公司通过支付浮动利率、收取固定利率的互换，将未来的浮动利率负债（如贷款）转换为固定利率负债。这样做的主要目的是对冲利率上升的风险，锁定未来的利息支出。选项A错误，此为对冲行为而非投机。选项B错误，策略是为了对冲利率上升。选项D错误，公司是希望减少而非增加利率风险暴露。七、A解析：根据线性关系假设，VaR与投资组合规模成正比。VaR=PortfolioValue*VaRRatio。原VaRRatio=$2M/$100M=0.02。新投资组合规模为$120M，新VaR=$120M*0.02=$2.40M。选项B是原VaR值。选项C错误，VaR随规模增加而增加。选项D错误，虽然需要知道波动率才能精确计算，但题目假设线性关系，且给出了比例。八、B解析：Gamma（Γ）衡量的是期权Delta值对于标的资产价格变化的敏感度，即Delta值的变化率。Delta本身衡量的是期权价格对于标的资产价格变化的敏感度。Vega衡量的是期权价格对波动率变化的敏感度。因此，Gamma是Delta的Delta，衡量Delta的变化速度。九、D解析：该策略是买入执行价较高的看跌期权（P45）并卖出执行价较低的看跌期权（P40），形成宽跨式看跌期权（BroadStraddle）。初始净溢价=收到的溢价-支付的溢价=$1-$2=-$1（净支付费用）。该策略的盈亏平衡点在两个执行价之间，具体为：盈亏平衡点=较高行权价+净支付费用=$45+(-$1)=$44。但题目问的是与合成看涨相关的盈亏平衡点，此策略是卖出看跌合成看涨（ShortPut,LongCall）。对于合成看涨，盈亏平衡点=较低行权价-净支付费用=$40-(-$1)=$41。因此，选项D正确。注意：此策略初始净成本为-1，盈亏平衡点为41。十、B解析：每日结算价从$50增加到$52，价差增加$2。初始保证金为$2,000，维持保证金为$1,400。维持保证金是初始保证金的70%($1,400/$2,000=0.7)。账户权益变化=$2*(52-50)=$4。新账户权益=$2,000+$4=$2,004。新的保证金比率=$2,004/(新结算价*合约乘数)=$2,004/($52*X)，其中X是合约乘数（题目未给，但在计算中会被约掉）。假设合约乘数为1，新保证金比率=$2,004/$52≈0.385。原保证金比率=$2,000/$50=0.4。新比率低于原比率，但高于维持保证金比率（0.7）。如果题目假设合约乘数为100，则新比率=$2,004/($52*100)≈0.0385，远低于维持保证金比率，会发生MarginCall。由于选项中只有$1,600的追加要求，且新权益$2,004远高于$1,400，且高于$2,000，因此严格来说不会触发MarginCall。但选项设置可能基于不同假设或简化，最接近的情况是初始权益增加，不会触发追加。重新审视，新权益$2,004>初始$2,000，大于维持$1,400，没有低于维持水平。选项B（追加$1,600）是不可能的。选项A（无追加，权益增加）最符合计算结果。此题选项设置可能存在问题或假设不清。基于标准期货计算，新权益$2,004>$2,000>$1,400，无MarginCall。如果必须选一个最接近“可能发生追加”的，可能题目想表达的是如果前一天结算价为$48，则新结算$50，权益$2,000+$4=$2,004>$1,400，无追加。或者题目假设了更高的合约乘数导致新权益低于维持水平。按最直接计算，无追加。假设题目意在考察MarginCall机制，需要新权益低于维持水平。重新审视，$2,004>$1,400，无MarginCall。题目选项可能错误。若按标准计算，答案应为A。但题目要求必须选择一个。可能在特定情境下（如更高乘数或不同维持比）会触发。按最简单情况（乘数1），不触发。选择A。十一、C解析：原前向汇率是1.10USD/EUR。6个月前向点增加50基点（bps）意味着现在需要支付更多的USD来购买1EUR，或者用1EUR可以换到更多的USD。增加50bps相当于增加了0.0050。新前向汇率=1.10+0.0050=1.1050USD/EUR。十二、C解析：Vega（ν）衡量的是期权价格对于标的资产波动率（Volatility）变化的敏感度。波动率越高，期权的时间价值通常越高，因为更大的波动性意味着更大的潜在价格变动可能性。选项A是Vega的定义。选项B是Gamma的定义。选项D描述的是Vega衡量影响，但不是其定义。十三、B解析：对于未行使的期权，其价值在到期时为零。如果期权的价值在到期时为正（即被行使），则持有者会行使期权，获得正的现金流。如果期权的价值在到期时为负或零，持有者不会行使，因为会损失钱。因此，如果swaption未被行使，其价值为零。十四、A解析：卖出（写）看跌期权（PutOption）收取溢价$4。如果到期时标的资产价格（$28）高于行权价（$25），则看跌期权不会被行使，卖方赚取全部溢价$4。因此，利润等于收到的溢价$4。十五、B解析：Cross-hedgerisk（交叉对冲风险）是指使用一种衍生品对冲另一种（通常不直接相关）风险exposures时，由于对冲工具与被对冲风险之间的不完全相关性而产生的风险。基差风险（Basisrisk）是指期货价格与现货价格之间关系（基差）的不确定性导致的风险，虽然也涉及价格关系，但Cross-hedg