期權(quán)期貨-復(fù)習題

B. A.內(nèi)涵價 B.時間價 C.內(nèi)在價值+時間價 D.有效價下列說法錯誤的是 )D.的因素表述對的的是(A)。 C.執(zhí)行價格越高，期權(quán)價值越 D.無風險利率越高，期權(quán)價值越【解析】B、C、D錯誤的是(D)。期權(quán)空頭價值為- B.期權(quán)多頭價值C.買方期權(quán)凈損益為1 D.賣方凈損失為-同價格的看跌期權(quán)，這事實上相稱于該投資者在期貨市場上(A)。A.做多 B.做空 C.對 D.套下列因素中，對股票期權(quán)價格影響最小的是 )A.無風險利 B.股票的風 C.到期 D.股票的預(yù)期收益的執(zhí)行價格為100美元，期權(quán)價格為5元。如果股價()，無視委托傭金，看漲A.漲到104美 B.跌到90美 C.漲到107美 D.跌到96美【答案】105美元以上才有利潤,105的凈利潤為()。(無視交易成本)。A.8.5 B.13.5 C.16.5 D.23.5【答案】如果期貨看漲期權(quán)的delta為0.4，意味著( D.期權(quán)價格每變動0.4元，期貨的價格則變動0.4【答案】格波動率的變化率，thetaGamma指標是反映 )的指標 【答案】6月1日，武鋼CWB1的Gamma值為0.056，也就是說理論上( A.當武鋼股份變化1元時，武鋼CWB1的Delta值變化0.056。C.當武鋼股份變化1CWB1Vega0.056。D.當武鋼股份變化1CWB1Rh0值變化0.056?！敬鸢浮吭O(shè)S表達標的物價格，X表達期權(quán)的執(zhí)行價格，則看跌期權(quán)在到期日的 A.Max[0，(S- B.Max[0，(X- 【答案】下列不是單向二叉樹定價模型的假設(shè)的是 )將來股票價格將是兩種可能值中的一 B.允許賣C.允許以無風險利率借人或貸出款 D.看漲期權(quán)只能在到期日執(zhí)【答案】【解析】D某公司的股票現(xiàn)在的市價60元1股以該股票為標的資產(chǎn)的看漲期權(quán)執(zhí)行價格為63元，到期時間為6個月。6個月后來股價有兩種可能：上升25%或者減少20%，則delta套期保值比率為( )。 【答案】c

12

75同價格為10.5元的該股票歐式看漲期權(quán)的價值為()元。 【答案】erTpud，

e

[pfu(1p)fd不發(fā)股利，運用布萊克一斯科爾斯模型所擬定的股票看漲期權(quán)價格為()。 【答案】 期貨交易中套期保值的作用是 ) 20.A:B:C:D:變二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％，浮動

六AB0.15％A6.85％B10.45％的

別為英鎊 英鎊

英鎊？英鎊英鎊英鎊 英鎊英鎊$5、$3和$2.如何構(gòu)造蝶式差價期權(quán).請用一種表格闡明這種方略帶來的盈利性.股票價格在八基于同一股票的有相似的到期日敲定價為$70的期權(quán)市場價格為$4.敲定價$65$6。解釋如何構(gòu)造底部寬跨式期權(quán).請用一種表格闡明這種方略帶來的盈利性.答案：buyaputwiththestrikeprices$65 buyacallwiththestrike$70,thisportfoliowouldneedinitialcostThepatternofprofitsfromthestrangleistheStockPayoffLongPayoffLongTotalTotalST65-065-55-65＜ST000-ST0 九遠期/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%。若在兩個月后預(yù)期支付的紅利為＄1.50，解S050X50r0.1,σ0.3,Tln(50/50)(0.1ln(50/50)(0.10.09/0.3d2d1

S0應(yīng)當是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位小數(shù)）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