期权期货-复习题

B. A.内涵价 B.时间价 C.内在价值+时间价 D.有效价下列说法错误的是 )D.的因素表述对的的是(A)。 C.执行价格越高，期权价值越 D.无风险利率越高，期权价值越【解析】B、C、D错误的是(D)。期权空头价值为- B.期权多头价值C.买方期权净损益为1 D.卖方净损失为-同价格的看跌期权，这事实上相称于该投资者在期货市场上(A)。A.做多 B.做空 C.对 D.套下列因素中，对股票期权价格影响最小的是 )A.无风险利 B.股票的风 C.到期 D.股票的预期收益的执行价格为100美元，期权价格为5元。如果股价()，无视委托佣金，看涨A.涨到104美 B.跌到90美 C.涨到107美 D.跌到96美【答案】105美元以上才有利润,105的净利润为()。(无视交易成本)。A.8.5 B.13.5 C.16.5 D.23.5【答案】如果期货看涨期权的delta为0.4，意味着( D.期权价格每变动0.4元，期货的价格则变动0.4【答案】格波动率的变化率，thetaGamma指标是反映 )的指标 【答案】6月1日，武钢CWB1的Gamma值为0.056，也就是说理论上( A.当武钢股份变化1元时，武钢CWB1的Delta值变化0.056。C.当武钢股份变化1CWB1Vega0.056。D.当武钢股份变化1CWB1Rh0值变化0.056。【答案】设S表达标的物价格，X表达期权的执行价格，则看跌期权在到期日的 A.Max[0，(S- B.Max[0，(X- 【答案】下列不是单向二叉树定价模型的假设的是 )将来股票价格将是两种可能值中的一 B.允许卖C.允许以无风险利率借人或贷出款 D.看涨期权只能在到期日执【答案】【解析】D某公司的股票现在的市价60元1股以该股票为标的资产的看涨期权执行价格为63元，到期时间为6个月。6个月后来股价有两种可能：上升25%或者减少20%，则delta套期保值比率为( )。 【答案】c

12

75同价格为10.5元的该股票欧式看涨期权的价值为()元。 【答案】erTpud，

e

[pfu(1p)fd不发股利，运用布莱克一斯科尔斯模型所拟定的股票看涨期权价格为()。 【答案】 期货交易中套期保值的作用是 ) 20.A:B:C:D:变二Explanationspeculatorswishtotakeapositioninthemarket.Eithertheyarebettingthatapricewillgouportheyarebettingthatitwillgodown.TheyderivativestogetextraHedgersareinterestedinreducingariskthattheyalreadyArbitrageinvolveslockinginarisk-lessprofitbysimultaneouslyintotransactionsintwoormoreAcalloptiongivestheholdertherighttobuyanassetbyacertaindateforacertainprice.Putoption:Aputoptiongivestheholdertherighttosellanassetbyacertaindateforacertainprice.Futures（forward）contract:Itisanagreementtobuyorsellanassetforcertainpriceatacertaintimeintheshortselling:Theinvestor’sbrokerborrowsthesharesfromanotherclient’saccountandsellsthemintheusualway.Tocloseoutthepositiontheinvestormustpurchasetheshares.Thebrokerthenreplacesthemintheaccountoftheclientfromwhomtheywereborrowed.In-the-moneyoption：itwouldleadtoapositivecashflowtotheholderifitexercisedrisk-neutralvaluation:Firstly,assumethattheexpectedreturnfromthestockpriceistherisk-freerater,thencalculatetheexpectedpayofffromtheoption,atlast,discountingtheexpectedpayoffattherisk-freerateFactorsaffectingstockoptionpricing:stockprice,strikeprice,risk-freeinterestrate,volatility,timetomaturity,anddividends.bottomverticalstrangle:abottomverticalstranglecanbecreatedbybuyaputwithlowerstrikepricesandbuyacallwithhigherstrikeprices.Bullspreads:Abullspreadcanbecreatedusingtwocalloptionswiththesamematurityanddifferentstrikeprices.Theinvestorbuysthecalloptionwiththelowerstrikepriceandshortsthecalloptionwiththehigherstrikeprice.Bullspreadscanalsobecreatedbybuyingaputwithalowstrikepriceandsellingaputwithahighstrikeprice.Bearspreads:AbearspreadcanbecreatedbysellingacallwithlowerstrikepriceandbuyingacallwithanotherhigherstrikeButterflyspreads:Abutterflyspreadinvolvespositionsinoptionswiththreedifferentstrikeprices:buyingtwocalloptionswithstrikepricesX1andX3,andsellingtwocalloptionswithastrikepriceX2,X1＜＜三.Explainthedifferencesbetweenforwardcontractandfutures contractbetween2parties Exchangetraded Usually1specifieddeliverydate ofdeliverydatesSettledatmaturity SettleddailyDeliveryorfinalcashsettlementusuallyoccurs

Contractusuallyclosedout tomaturity四.Explainthedifferencesbetweenexchanged–tradedandOver-the-counter?Exchangestandardtradingfloororcomputervirtuallynocreditnon-standardtelephonesomecredit五0.8％，浮动

六AB0.15％A6.85％B10.45％的

别为英镑 英镑

英镑？英镑英镑英镑 英镑英镑$5、$3和$2.如何构造蝶式差价期权.请用一种表格阐明这种方略带来的盈利性.股票价格在八基于同一股票的有相似的到期日敲定价为$70的期权市场价格为$4.敲定价$65$6。解释如何构造底部宽跨式期权.请用一种表格阐明这种方略带来的盈利性.答案：buyaputwiththestrikeprices$65 buyacallwiththestrike$70,thisportfoliowouldneedinitialcostThepatternofprofitsfromthestrangleistheStockPayoffLongPayoffLongTotalTotalST65-065-55-65＜ST000-ST0 九远期/FSer(Tt)(SI)er(Tt)Se(rq)(Tt B-S公式的使用cSeq(TtN(dXer(TtN(d pXer(Tt)N(d)Seq(Tt)N(d d1

ln(S/X)(rqσ2/2)(T

d2d1

TσTσT2).Supposethecurrentvalueoftheindexis500,continuousdividendyieldsofindexis4%perannum,therisk-freeinterestrateis6%perannum.ifthepriceofthree-monthEuropeanindexcalloptionwithexerciseprice490is$20,Whatisthepriceofathree-monthEuropeanindexputoptionwithexerciseprice490?byput-callWhatisthepriceofaEuropeanfuturesputoption：currentfuturesprice$19,thestrikepriceis$20,therisk-freeinterestrateis12%perannum,thevolatilityis20%perannum,andthetimetomaturityisfivemonths?（2Solution:InthiscaseF=19,X=20,r=0.12, T-σTd1σTd2d1N(0.33)

N(0.46)N(d1)N(0.33)0.6293,N(d2)N(0.46)ThepriceoftheEuropeanput pXer(Tt)N(d)Fer(Tt)N(d Aone-year-longforwardcontractonanon-dividend-payingstockisenteredintowhenthestockpriceis$40andtherisk-freerateofinterestis10%perannumwithcontinuouscompounding.WhataretheforwardpriceandtheinitialvalueoftheforwardSixmonthslater,thepriceofthestockis$45andtherisk-freeinterestrateisstill10%.Whataretheforwardpriceandthevalueoftheforwardcontract?Theforward

FSer(Tt)40e0.144.21Theinitialvalueoftheforwardcontractiszero.f(a)ThedeliverypriceKinthecontractis$44.21.Thevalueoftheforwardcontractaftersixmonthsisgiven:fSKer(Tt)4544.21e0.10.5Theforward

FSer(Tt)45e0.10.5310%，30%。若在两个月后预期支付的红利为＄1.50，解S050X50r0.1,σ0.3,Tln(50/50)(0.1ln(50/50)(0.10.09/0.3d2d1

S0应当是0S501.50e0.16670.10X50r0.1,σ0.3,T

ln(48.52/50)(0.1ln(48.52/50)(0.10.09/0.3d2d1

12%，30%，3S052X50r0.12,σ0.30,Tln(5250)(0.120.32/d1 0.30d2d1

5%，35%，6S069X70r0.05,σ0.35,Tln(69/70)(0.050.352/2)d1 0.35d2d1

十Consideraportfoliothatisdeltaneutral,withagammaof -5,000andavegaof- Supposethatatradedoptionhasagammaof0.5,avegaofandadeltaofAnothertradedoptionwithagammaof0.8,avegaof1.2,andadeltaof0.5.Whatpositioninthetradedtwocalloptionsandintheunderlyingassetwouldmaketheportfoliogamma anddeltaSolution:If,w1,w2, aretheamountsofthetwotradedoptionsunderlyingassetincludedintheportfolio,werequire-5,000+0.5w1+0.8w2=-8,000+2.0w1+1.2w2=w3+0.6w1+0.5 =>w1=400,w2=6,000,w3=-=>Theportfoliocanbemadegamma,vegaanddeltaneutralbyincluding400ofthefirsttraded6,000ofthesecondtradedoption.Andshort3240underlyingasset. 1）

N(d2)

X

2T f

1, T

TlnS~NlnS(rσ2/T

T

p(STX)p(lnSTlnX)1p(lnSTlnX1N

lnXlnS(rσ2/2)(TσσTσTσT

lnXlnS(rσ2/2)(T

)N(d2

X

2SinceT

f

1,

2and

N(dT T E[

]KP(S1XS2 1, K[P(S1X)*P(S2X)]

fer(Tt)E[f]er(Tt)K[N(d)*N(dln(S1/X)(rσ2/2)(T

ln(S2/X)(rσ2/2)(T

,dTT

,TT12、Usetwo-steptreetovalueanAmerican2-yearputoptiononnon-dividend-payingstock,currentstockpriceis50,thestrikepriceis$52,thevolatilityofstockpriceis30%perannum,therisk-freeinterestrateis5%perannum.（保存2位小数）Inthiscase,S=50,X=52,σ=0.3,Δt=1,r=0.05,theparametersnecessarytoconstructthetreeareu

d10.74u

=1.10p 0.51,1pufi,

ert[ (1p) 2i1.j i1.0 Ifastockprice,S,followsgeometricBrownianWhatistheprocessfollowedbythevariableS geometricBrownian

Show

S Theexpectedvalueof

E(S)Seμ(Tt).WhatistheexpectedvalueTS?nTS?TThevarainceofST

D(S)S2eμ2(Tt)(eσ2(Tt)1)TS?TWhatisthevariance TS?TUsingrisk-neutralvaluationtoval