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1、FRM一级模考试题（二）1.Inthe1980s,BankersTrustdevelopedindexcurrencyoptionnotes(ICONs).Thesearebondsinwhichtheamountreceivedbytheholderatmaturityvarieswithaforeignexchangerate.OneexamplewasitstradewiththeLongTermCreditBankofJapan.TheICONspecifiedthatiftheyen-USdollar
2、exchangerate,ST,isgreaterthan169yenperdollaratmaturity(in1995),theholderofthebondreceives$1,000.Ifitislessthan169yenperdollar,theamountreceivedbytheholderofthebondis⎡⎛⎞169⎤1,000-max⎢0,1000，⎜⎟−1⎥⎣⎝⎠ST⎦`Whentheexchangerateisbelow84.5,nothingisreceivedbythehold
3、eratmaturity.WhichstrategybelowcorretlydescribesthecombinationofICONs.A.Aregularbond,alongpositionin169,000yencalloptionwithastrikepriceof84.5yenperdollar,ashortpositionin169,000yencalloptionwithastikepriceof169yenperdollar.B.Aregularbond,alongpositionin169,
4、000yencalloptionwithastrikepriceof169yenperdollar,ashortpositionin169,000yencalloptionwithastikepriceof84.5yenperdollar.C.Aregularbond,alongpositionin169,000yencalloptionwithastrikepriceof169yenperdollar,alongpositionin169,000yencalloptionwithastikepriceof84
5、.5yenperdollar.D.Aregularbond,ashortpositionin169,000yencalloptionwithastrikepriceof169yenperdollar,alongpositionin169,000yencalloptionwithastikepriceof84.5yenperdollar.Answer:ASolution：假设日元的在ICON到期日时的汇率是S,（日元/美元），那么从ICON获得收益：1000如果S>169T⎛⎞16910001000−−⎜⎟1如果
6、84.5≤S≤169T⎝⎠ST0如果S<84.5T169000当84.5≤≤S169时，收益可以写成：2000−TSTICON的收益是来自以下方面：(a）定期的债券，(b）以l/169的执行价买人169000日元的看涨期权的空头，(e）以1/84.5的执行价买人169000日元的看涨期权的多头。如下表所示：债券终值看涨期权空头终值看涨期权多头终值总头寸终值S>1691000001000T84.5≤≤ST1691000⎛⎞11016900−−16900⎜⎟2000−S169ST⎝⎠TST<84.51000⎛⎞11
7、⎛⎞110−−16900⎜⎟16900⎜⎟−S169S84.5⎝⎠T⎝⎠T2.Supposethatsterling/USDspotandforwardexchangeratesareasfollows:Spot1.608090-dayforward1.6056180-dayforward1.6018Whatopportunitiesareopentoanarbitrageurinthefollowingsituations?(a)A180-dayEuropeancalloptiontobuy£1for$1.5
8、7costs2cents.(b)A90-dayEuropeanputoptiontosell£1for$1.64costs2cents.A.Gain;LossB.Gain;GainC.Loss;LossD.Loss;GainAnswer：B．Solution:交易者买了一个180天的看涨期权，并且同时持有一个180天远期合约的空头。那么，如果ST是期末的汇率，那么这份看涨期权的收益是：
