Solutions for Options, futures and derivatives

《Solutions for Options, futures and derivatives》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

11.1.aIStwoormorenotanotsomeonetoanassetItasomeoneIta 2areareis(IIScentsIS51cents 3oneISa 4s1.13642StockPrice04-----------�------------�----+_----�----------�-4ifIS 51.1464StockPrice-8rateis'-''''�.n'''F,'"'rateis 6usecontracttoonetont�'r",,('tratesratesanISsumiszero.contractassetatcontractismaxISmaxrateatisI,if1,1,1)if0ifwasatypointhefirstofthebook.The1,000-1)1. 7SlAssetPricecananIStoanIIItoan 81IScontractattwocontractsisth.'rAtrwAFd+11,itisb>ac.rateisR(1+12R12(1+rateisannum.rateisR12or1)=1218R $1IS,Ov+15.1'2.0)'++1y=or111=d=1.015+A3textas(1aa1.5+I3ISratesareas5.1 24[I,oraone0:10:-1toraleisI10orannum.Ifratesweretermstructuretotermratesaretermstructure reasons4.1),IS1+Ix2++IIx4+1IIS11+2XIIx2+3XIx3+4x5X1 onaIStoISI08x:+I08x4+IlOilx:'i+ISansweris21+=1R=113or11 accountassetcontractIS12x05IIS.}0--,,,,1'+xO.3333 toIScostisTistocontract.isI)as:orLHu""".rl1contractiszero.j=itisxO.S1or1. SIXISx05=Ior$11.2+2x3t67orisistooI.contractscontractsareIS ancostsareor1xO.7:i+itisounce.-II)>anal.contractmaturesatI)2.contractmaturesatt2contract.-11)isatcannotcontract.a 31contract5.14rateisanrate10zeroacontractatTISII.Itzeroqisexcessreturn<·V__T..".",rateasx.returnisr+xx-Ittoisasset.assetat 32contracttoatT.0:T:TmustorN tisF;=5,is11.IS-F;)+ISis11=IShis,,,,,,,,,..,,.viscontracts.contracts5 o$15mostrecent6contract rateis3or3acontractis1xl,$1contractsISx7.6tonearestcontractsisxlOcOJnp'0U11ae�areturnis6x181 is1I12.ISII12+3113or$11ISoneISwexI4isCl1l�a[,estto41110+x1contractifcontractwereon(liifcontractwere11 37Ifoutcomes.orassumesrateisassumesnorateis4xor3rateis11or))"'-'.,,"',"to91isnotnet::ae,Q. 38contracts----x2tonearest10contractstonearestcontractsanswer7.1toxor5Icontracts.aresame. 39contractannum.rateanII,ISreasonsseuleaatnot 7.1 41IS(xcontractsisthprptr.rp$1.161+=$1 42IS16(Itox1x1ofISis-$1$1.716tooverto 437.93SIXwecost 441.ratesareTratesat6are234 457.12annum,Batarrowsatcontracts.orYisratesoccurs:occurs: 46aISIx+xIfxyaonatoratesareazerorate-O,05xO,51.01.5x2,S 47rateisannumxU+x),Oare Chapter8MechanicsofOptionsMarketsSOLUnONSTOQUESTIONSANDPROBLEMS'fl1�Ilvn',"mak�S:lP".>ti'if,ht'I"keof,ho!"oc�>It,hec.'p;';,lion,):,10:"1.1cs.,11�1IlS:'7.Inlhe,;;:CllCunm;'IC<'.Ics�,ll:In�O'",henlatunly;n'·��I()I·.pwii'.....ilhIll(.1....:1..!'riC':inFi&IJ'"S8.1Prublemg.!.TIle1I1VC'>I<>rno:o;.o:".Ibeo::��r�i,e,I,.,rId'hc1n",,�I,)fmaJ.-e.:>1'1',61i)f�.!fII.:,.llOCI..pric�ISbc""cen�50and$.5<1.Ih(:ophol1I�nClc,,�dalldIheIrWt'SI(>(mal.."aI'h'lilbet",,,,·"-)I):lndSA.The��ri;ll1011,'f,hem"�Slor'sprofllWllhIll;.'>Ie..:!':plltci.,ib,hov-'nInr:i�u":$$2Fi::ul'l'.StUInVeilor'sprofllInl'rr,.t.le",SI6Profit1$)5I.132StockPrice(S)11a.-------'�.----,-13:,antllheopliong.ivcs.Iheholderthcrighttopurchasetwiceasmanyshares, 50Chapler8.Mecl'1an,cs01Option!;MarkelSPrtlhlclIl11.7.E."c�uricsroc"or!iOIl�1;",illonglime(often10�C,lf'01mOle).'nrcrcI�:I'C�lll1gI'l.'noddllnll�......hkh[heopll)n,(:InOOtPeI'H'n:IM!tlIfthec),C:uhvele;,c�thecompanydllnngthevc,riugperiodlh�lpllrl1lan::iorielled.Ifthe",)"cculivc1c.J'e�thecompanyafl":!Ihc('l1dofthl'e�llIll!pcriou.irHh<:·moncyoption,Jrt"c:-;,cr'i-;cdimnwdiah!lywllikoll-oi-th<:-IIlOIlCyortl(ln�.m::forfeited.TheOPIIOn>c:mllOlbe�()Id10i.llll>lhcrpanyhytil"....>.cculive.I'r<.ohl('lllX.Ii.TIrePhrlad('iphrJb.ch:mgcoIT,''''Eurof�:;lnand."'.rno.:riCJlloptlOll�wlIh,1;mdllrd,trikepri,".::,;lIldIiml'."1Ili.lIlJrlI).()PIiOll'IIlilt"0'1"1·thc-coun[("Immkelh1.l"ctheadvantageIhn!Ihe>canIx-1,J1or�'J('1m�'llht-prcci:;e11·...d5.ofthetri.":l:'l1fcr,'1('irurs.l(jvlIntngc:i�th:ltlhcyL'po�{'thtIr{'asurertosomecrcdrtrisk.f::x{"h:mgesorg:lniz,:theilImdmgsotha!th....l!i:-.vinunllynocrt'"{htri�l-..Prohl<.>m8.'1.IgnOringthetimev;ilU:ofmoney.the-holde.roi11K'opli"l1willmakaprOfitifthe�tockpric....atmatuntyoitheoplioni�greaterthan$105.Thisi�!lccau","thepayoff10IhelIolu..'1oftheoption1�.inIhL'�'clrcum>lancc�.greaterlh3nlheS5paidfortheoption.Theoptionwillhi.'c.>;crciscdIfthl'�tockpncl!almaltlrityisg�a4:rthan$100.NOI'::IhatIithe�tockI)lkeisr...:1�{'enSIGO:md$105111<.'optl.:>n1�ccro)cu,htHIheIwldl'roftheoptionl:Ioke:;.a10%0·er311.11k:prontfwmalongp�ilionI�:I..�sho�ninFIgure58.3.Prohl<.>m8.10.Ignoringthelimevalu....of11oney.the-sclk'roftll('opliollWillmake;1P'lOliliithl'stockpriceatmalurityISgn!aterthanS52.00.Thisbh...·cau�thecost10the�dkroftheopl1onl�inIheseClrcumstanccsIe�sIh:l.1llhepri..:cTlX"cll1co101tiK'oplion.Th..:oplionwillix'e<:I-..:iscclifthe�tockpriee:unmmrityISlessIh:,"$60.00.Nm.·thatifthc,lockpri..:ei..ix·,.I,·cl·nS:'200and:5.60.00theselleroftheoptionmnkcs:1profitcventhoughIheoptionisCxelc'lsed.TheproiitfromIh..:�hon�illonis:l..'ShOWll1llFigureSS.4.Th.::tCTminalvalueofthelongfO["'.'I.r:m1pncc(Ifthea..�::..c:.·tatIhetimetheportfoliois-.elup(TheoeliverypriceintheforwardCOlllracti)abQrit.)ThetermiMIvalu('01thepUIoptioob:TheICTlninalvalueoftheportfoliOI�til<:r<:fOl"e!h-['IJ+max(F�-.)7.0)1 51FigureS8..3:ProlllfromlongposilioninProblem8.9205·10=111>«0,ST-/'0)'nlisistheS;Jmeasthe.terminalv:llueofaEuropeancalloptionwiththesamematurityastheforwardcontractandane.xercisepriceequaltoFo.ThisresullisillustratedintheFigureSS.S.WehaveshownthattheforwardCOlllraclplustheputisworththesameastlcallwiththesame:mikepriceandlime10malUrilY,1$Ihepu!.TheforwardcormaCIisworthzeroatthelimeIheportiolioissetup.l!followslhattheputisworththesameasthecallatlhetimetheportfolioissetup.Problem8.12.FigUf!S8.6showsthevariationofIhetrader'spositionwiththeassciprice.Wecandividetheaitemalivt;!'[IsseipricesintoIhre�ranges:(a)WhenIheassetpricelessIhan$40.theputoptionprovidesapayoffof40-SyandIhecalloptionprovidesnopayoff.Theoptionscost$7andsothetotalproHIi�JJ-Sr.(b)Whentheassetpriceisbetween$40and$45.neith�roptionprovidesapayoff.Thereisanetlossof$7. 57Chapter8.Mechanics01OpllOnsMarkelsFigureSs.�.Profilfrom,honpo�LlmninPr<..mh.:mR.IO<1,IUFigureSS.5:Profit(rom1x}r1fohoinProblem�,II..'."",'"',,'""",,',"f",wa.d"Pili-1fll.,1 53-FigureS8.6:ProlllfromtradingstrmegyinProblem8.2Callrut-Tot:,!",'10,','s......""S�clI'ri..:cO+--------.���--r_----�_r�----�2"00"-5,J0(c)Whentheass.etpricegreaterthall$45.thecalloptionprovide:,apayoffofSf-45andthepmoptionprovidesnopayoff.Takingintoaccountthe$7costoftheoptions,thetotalprofitisST-52.(d)Thetrade.rmakesa.profit(ignoringthelimevalueofmonl.'Y)ifthestockpriceislessthan$33orgreaterthanS52.Thistypeoftradingstralegyisknownasastrangle.andisdiscussedinChapler10.Problem8,13,Theholderof"lJlAmericanoptionhasallthesamerightsastheholderofO[(,lIli:11payuffI';.'iT-K.ThedLfien!n.::1'I'IhatfvrawrllenpUllhe,:ounlt'rpan�ch()(I"l''''whetheryOIigl'l[hl'p:L�o(f(andWII!allow}OUI,)gel11onl�\.-hcn11i<.'lCgalL'i.'1Oyou).Foralllngcall�UIIMCldc.....hl.'[!tayouge[IhepiLyvff(alKyouchoo�10�eltwht'lli[i�pl)sLtivi."10you),Prohlt'lII8.1f>.Forv::lrdC()nll:lCl�locI;inthcl'�'hango:rmcIh;1Iw[1I:Ippl)10,jpanicul:l.Ilr:ulsx·,ion1·1!Iure.OptIonspro'idcin�ul;mccthtll11'1<(').,changer:Llc\Oll!nullx'worseIhallSA)nekH'1.TheadvanlOl�cof:1forw:ml(OfI1l�1C1I�lhalunccn:l1nlyI�('ltmin:lleua:.f:1taspossibleThedis!I,h'ilnl:lgcISIh:1IIh!.'OUIc.omcwilhhedgingcnnbe.-sil:!niflC�lIl1ly.....Or'il�IhanliltOUlCQl1le-.vilh110hedc;in(!.Ttn�dls:lI.h,UlI:Ige1�!Lotasm:lrkcdwilhoplions.Howe'cr,unlikeforwardl:Qnlr:LCIS,oplionsProhk:m8.17.(a)Tht:'opliollconll:tCIIX'colII('one[0bu�500)(1.1=550sh:tr...�wilhan(,"}(crciM'price.10/1.1=�(I:.6.(h)Thcrei:.nodft'ctThi:lemlSof;Illoptionscon[raCIarcflOInomlal1y;mJI�ledforc;l�hdividend>.(c)Theoptioncontr.lcli)('.c(lllIc-Son..:Itlbuy500.<,I:0:2.0()Oshnf('swithanexercIscpriel"of,10/.1Prl'lh�1l18.18.111c(:}(ch:lII�<:h:'l,...ct:namruksg(w('ming.wh<:nIr:.dingin;1newoplioni>initinIL'{I.TheSt'meanIhat11lr:llptioni�c1o-:e-lo-the-moncywhenilislirstltalk'd,Ifallcalloplion�areinthi:m,.""tr.'"A annum.-1anretumJ.L1.is++Bare-t)+x 1(jisratetouseisrate.caseKr1,(jT17isxor rcase14ISIxO.:?5xx3orancasepratereturnovera-2¢15-)¢11returnis11annumis]annum.16 84ISI-N=1IS(l+(J+1'-12l'+Iannum. 1.f,(I5+(11-2(Tf)aISt)at5+-f+-5+L.."''''''''is+-t)-rfis isto12.1I11/++-2ISt=T.=1T.Itcanht-1)I)--h2tois11=1)+kkisaconstant.tkso1)I-1)]-t)II+-2or-t)caser=T IS12xO.25NorcaseKr(JT=isor1xo.13J)=1-1-<1-)ItisnevertoAn••"....is1 -------==---ita)ISf)t)------==='"---t) 89c)-I))-I)+it)we".lla.H1(J-++-)--�+2rca 90 text'I'2=Tr=K-12)]67)K[1(1-AntooneIS 95s0.83230.03230.79970.00000.00670.76830.0000case,K=ra=18,Tq18isorlL15. 96contract.IScaseKr12,TisxO,6667I)x06667xxreasonisaAaaatinterestrate.caseu=1.12danmovementaIS1-112-ISx6+xKrT= is167x-19=1or$1itcanreturncontractsKr=(j=Tqcan(lxO.2SXp=itisiscare:at ISxO.5_1xO.)isK=10l:"roDlClm1caseq=rTK=ccorPc+xO.06x0.04P10+3ISon:IS$contracts ratetoxtocaseanamount ifISisIxO.1667ifISIS--K7ifISISIxO.:l333ifISISK3caseanmoveis1.1caseanmoveis1.1ISp3+ 1to72.600066.000012.60006.175360.000059.40003.02650.00003.02650.00000.000048.6(X)00.0000to0.00000.000059.400048.6000111.4(X)0 1(lII)c-parecaseKrI,TcaseK()rT=pcase=2+IxIc+IxIp+=2+tooneIS)1=1+ 103KISsameascanitisnotatCPmustC4wemustPorVUlt""isversa.maxc 104orcmaxp+>orwep.IfISatBr)'SKKISat1:.cKAismorearetoBisAismore 105AismoreBsopcKcpC+KorKaretoDisoismoreCppCPor-KCP< 1)6onanamountKatonanamountatinterestrateacontractT.contractsascontracts..IfISatBK-K+KisatT.Aisc+KAismoreIfaretoI]Bis++AisAismorep+c+K