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Springer Finance PDF

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SprinFgienra nce Editorial Board M.A vellaneda G.B arone-Adesi M.B roadie M.H.A. Davis E.D erman C.K liippelberg E.K opp W. Schachermayer SprinFgienra nce SprinFgienran ciesa p rogramomfbe o okasi meadts tudeanctasd,e micansd, practitwioornkeironsng i ncreasitnegclhyn aipcparola chteots h anea lysoifs financimarakle tsI.t toc ovearv arioeftt yo pincosot,n lmya thematical aims financeb ufto reiegxnc hangetse,rms tructruirsmaneka, g ementpo,rt folio theoeqruyi,t dye rivatanidv fiensan,c ieaclo nomics. A nn,C reditR isVka luatMieotnh:od sM,od elsan,d Applica(t2i00o1n)s M mma BaruccFii.n anciMaarlk etsTh eory: EquilibEriffiucmi,en canyd Informati(o2n00 3) E. Bingham R.K ieseRli.s k-NeVuatrallu atPriicoinn:gan d Hedginogf F inancial N.H and Derivative2sn,dEd itio(n2 004) T.R.B ieleacnkid RutkowsCkire.d iRits kM:od elinVga,l uatanido Hned ging( 2001) M D.B rigoa mdF. MercurioI,n teresRatte ModelsTh:e ory and Pracbce( 200I ) R.B uff,U ncertaiVno latiMlodietly-s Theory andA pplica(t2i00o2n) R.A-.Da na and Jeanblanc,F inanciMaalr keitsnC ontinuToiumes ( 2003) M Deboecka nd Kohone(nEd itorsV)i,s uEaxlp loratiionnF si nanwicthe S elf­ G. T. OrganizingM aps( 1998) R.J.E lliaontdPt . EK.o ppM.a thematiocfsF inanciMaarkle ts (1999) Gemon, Madan,S. R.P liska Vor(sEdti torMsa)th,e maticaFli nance­ H. D. and T. BachelCioern gress2 000( 2001) Gundlach Lehrbass (EditoCrsred)i,t Rlski+nth eB ankinIgn dus(try2 004) M. and F. Kwok, MathematicMaodle lso fF inanciDeriavla tive(s1 998) Y.-K. Kii/pmonIrnra,t ionEaxlu berance ReconsideThree Cdro:s sS ectioonfS tockR eturns, M. 2ndEd itio(n2 004) A.P elssEeffirc.i enMte thodsf oVra luiInngt eresRatte Deri vative(s200 0) J.-PLri genWte,a kC onvergencoefF inancMiarakle ts( 2003) B.S chmiCdred.i tRi skPri cingM odelsTh:e ory and Practic2end,Ed itio(n2 004) S..ES hrevSet,oc hastCiacl cuflouFrsi nanceTh e BinomiAasls ePritc ingM odel( 2004) 1: S..E ShrSevteoc,h astCiacl cuflouFrsi nancIeIC :o ntinuToiumes M-odels( 2004) YorE,xpo nentiFauln cbonoafBl roswn ian Motioannd RelatProcede sses( 2001) M. R. gs,tlnterest-ManRaateg ement( 2002) Za Zhu and ChernDeri,v ativSeec uritianeds D ifferencMee thods( 2004) Y.-1. 1-L A.Z iegleIrn,c ompllentef onnaboannd HeterogeneBoeulsi ienfC so ntinuToiumes - Financ(e2 003) A.Zi eglerA, G ameTh eory AnalyosfiO sp tioCnosrp:o ratFei nancaned Financial IntermediaitniC oonn bnuoTuisme ,2 ndEd iti(o2n004 ) StevEe.S nhr eve Stochastic CalcIuu sf or Finance II ContinTuiomuMeso -dels With 28 Figures �Springer StevenS hreve E. DepartmeonfMt a thematiSccaile nces CarnegieM elloUnn iversity PittsbuPrAg h, 15213 USA [email protected] Scanv on der Deutschen Filialed er staatlicheBna uerschaft (KOLX03a)' MathematSiucbsj eCclta ssifica(t2i00o0n)6 :0 -016,0 HIO6,0 1659,1 B28 LibraorfyC ongreCsast aloging-in-Publication Data ShreveS,t eveEn. Stochasctailcc ulfuorsfi nanceS teveEn.S hreve. I p. - (Springfienra ncsee ries) Incelmu.db eisb liograrpehfiecraeln acnedis n dex. Contenvt.2s . C ontinuousm-otdiemles . ISBN0 -387-40101-p6a per) (alk. I.F inance-MathemmaotdieclaslT- extbook2s.S. t ochasatniacl ysis­ TextbookIs.T. i tleI.IS .p nngefirn ance. HGI06.S52700 3 332'.01'51922-{lc22 2003063342 ISBN0 -387-40101-6 Pnntedo na cid-fpraepee r. 2004S pnngeSrc iencBeu+s ineMsesd iaI,n c. © Alln ghtrse servTehdi wso rkm ayn otb et ransloartc eodp ieidnw holoer i np arwti thto u thew nttepne rmissoifot nh ep ublis(hSeprr inSgceire nce+BusMiendeisasI, n c, 233 SprinSgt reeNte,w YorkN,Y 10013U,S A)e, xcepfto rb nefe xcerpitncs o nnectwiiotnh revteowrss cholaarnlayl ysUissei. n c onnectwiiotnah n yf ormo fi nformasttioorna agned retrievealle,c troandiacp taticoonm,p utesro ftwareo,r by similaorr dissimilar methodolnoogwyk nowno rh ereafdteevre lopiesfd o rbidden Theu sei nt hipsu blicaotfit orna dnea mest,r ademarskesr,v imcaer kasn ds imiltaerr ms, eveni ft heayr en oti dentiafises du chi,sn ott ob et akeansa ne xpressoifoo pni niaosnt o whethoerrn ott heayr es ubjetcopt r opnetnagrhyt s. Printientd h eU niteSdt atoefsA merica. 9 8 7 6 5 4 3 2 springerocnolmi ne To my students This ipnatgeen tlieobfnltaa lnlky Preface Origionf T hisT ext This htasee vxotfl rvmoeamd t hecmoautirinsc eMstsas h teoeS frc iienn ce ComputFaitnia(onMncSaepCl rF o)g arCtaa mr nMeeglUilneoi nv Tehres ity. conottfeh nbitos oh kasb eens uucsceewdsi sstfthuu ldwlehyno tsse math­ emabtaiccksg croonuosncfida s ltcasun cldau lsc ulpurso-bbaTasbheiedl ity. tegxti pvreessc tiasteoe fm ern,pet lssau ulsatirsbgiusmla,ein entdvty se onm e pro,bo ufmtso riem poritnaitnvueteixl tpyl,a dneavteialononrdpse e fidn ed through ecxlpaseswrriioteohnmm ca teth eairrpsier a olvE ixdeercdco.in s­es cluedveec rhya pStoemoretf. h eesxett ehntedh eaonrdy aortdehr earwsn fropmr acptriocbialqnleu masn tfiintaantciev.e Thfier tshtrc ehea ptVelorusmIh eao bvfee u esnie andh a-lsfemester courisnte h MeS CpFr ogTrhafemu V.llo lu mIhe as b euesnie nadf ull­ semestietnrh ec oCuarrsnBeea gcih'epes rl oMogeirrlCnalo mom np utational FinanVcloeu.Im Ie dweasv etlsoou ppetpdho rrheat-el s femceosutirensr e s thMeS CprFo gram. Dediciaotn Sicnieti sn ceip1nt9 it9o4hCn,ea rnMeeglMilaseot 'nep srr ogirCnao mm pu­ tatioFnianlha asng crea dhuuantdeorsdfet dutsdsT eh.ne pseeo,w p hlhoea ve cmoefr oamv aroiefed tuyc aatnpidro onfaelbs ascikodgnshra,aol bvu eene n aj otyot e aTchheh.ya b veee n teolae gaaserkrniq ,nu ge stthisaottni sm u­ lattehdi, nw koirnkgintgou nhdaerrtdshm teaa tnebdro ittahhle oretically and rpactaincodaft lerlenyq ,ut ehset iinongafc d lduisttioiop.oMni na cansly cmaefr otmeh fi nainncdeu asnwtder gryre,a ciisnoh uasr ing their knowledge iwna ytsh at enchlaasnscerexodpo emtfr hoiaer.el nlce Thtiesax ntmd y o wsnt oorfke n owhlaebvdeegn ee gfirteeadt ly from ientracwtiitteohh n MsSs uCtdFte sann,Id cotnlote ifanrrutonehm M e S CF VIIIP reface alu.m nIit htoiapskp eo rttoeu xnpigrtreyas tsti ott huesdsteeu daenndt s fromsetru dbeydn etdsi tchawitositr ntokgh em. Acknowledgments Converwsisatethvi eornasil n cplmeuyod piclnoeglD, la evHaiegdaau tnehds DmiKtrraym hkaoivvne,fl utehntice.seLx dut kKasrzur ke ad otfmh uec h manusacnprdri opvntiu dmeedr ousa ncdo mcmoOertnrhtseestcr ut dieonntss. anfdau clhtaypv oei onuteter dr ors ini mapnrdo voseefuam gregnletisset re d drafttshw ioosrSf ko .mo etf h easrJeeo naAtnhdaenNr astohnCa,an r,it eelr BogdDaony tcDhaivGnieodvr ,mS atneG,v ielnl KiasrJpeailne eS,ce eakn, JonAensa,Kt aorloiDl aivKkiop,dri A ,n drKzrea,ju sRLeaeilm bPiettcro , LukSsearnMg,ye ayg cNhiiclkoiv ,RI assmaSuaonscnM,s ias esni,Tm asos an­ So,lD eatvWihdi taankUdew Wrey stIusnpo .cm ase,e u ssoetfrhs ee sarel ier drahftassv ueg geexsetroecredi x saemsap nltdeh sce,oi nrt rairbaeuc t­ions knowlaetad pgperdo priitnah tteee. T x otpa oltilhn owtshsaeo i dietndh e develootfph mtiee,snx ttIm oagsmrt a teful. Durtihcnerg e atthitioe,sntx htoef waasup tahrotsriu aplpbloytyr h tee d NationFaolu nSdcaiteginrocaDnenM tSu8s-n0 9d2eD4rM6- S410,01 34a8,n d DM-S099113A1n.oy p infiinodn,is n,cag onsnd clourrs eicoonmsm endations expriens mstaehtdiea srrt ieha oolfs et haen ddaon u ontteh coerrs esflaercitl y thvei eowtfsh N ea tionaFlod uanSt.ci ioennce PibtutrsPgehn,n syUlSvAa nia, SteEvS.eh nr eve Apr2i0l0 4 Contents GenerParlo babTihleiot.ry. y . . . . . .1 . . . . . . . . . . . . . . . . . . . . . . . 1 . 1.I1n fiPnriotbeaS bpialcietsy . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.R2a ndVoaimra balnDedis s trsi..b.u.t.io.n. . .7. . . . . . . . . . . . . . 1.E3x pec.t ations 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14. ConverIgnetnle.csg er. a o.f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.C5o mpuotEfax tpieocn.t a.t.i.o.ns. . . . .2.7. . . . . . . . . . . . . . . . . . 1.C6h aonMfge eas u.r e. . . . . . . 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17. S ummary . . . . . . . .3 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.N8o t.e s. . . . . . . . . .4 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19. E xercises . . . . . . .4 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inforimoaantn dC onditio.n i.n g. . . . 4.9 . . . . . . . . . . . . . . . . . . . . . 2 . 21. Inmfaotrainodn u-algebras . . .4 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.I2n depe.n.d.e.nc.e. . . . . . . . .5.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.G3e nCeornadli Etxipoenca.tl a .t i.o n.s . .6 6. . . . . . . . . . . . . . . . . . . 2.S4u mm.a r.y . . . . . . . .7 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.N5o t.e s. . . . . . . . . .7 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.E6x ercises 77 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BrownMioatn io.n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3 . 3.I1n tro.d.uc:.t ..i. o..n . . . . . 8.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.S2c aRlaenddW oaml. k s. . . . . . .8 3. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 S.ymmReatnrdiWocam l. k. . . . . . . .8.3. . . . . . . . . . . . . . . . 3.2I.n2c reotmfhe Sneyt msm ReatnrdiWocam l. k. . .8.4. . . . . 3.2M.a3r tiPnrgoapfleoterrhS t eyy m metric RandWoaml. k . . . . . . .8 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2Q.u4a dVraiarattioictfo h Sney mmetric RandWoaml. k . . . . . . .8 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2S.c5aS lyemdm ReatnrdiWocam l. k . . . .8 6. . . . . . . . . . . . . . . 3.2L.i6mg iD tirisintbouttfhi Seoc naR laenddW oaml. k .8 8. . . X Contents 3.2L.o7g -NDoirsmtaraslit bhLueit moiitfoth n e BinoMmoid.ae ll. . . . . . .9 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.B3r owMnoita.in o .n . . . . . . .9 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13 D.efinoiBftr ioownMn oitaino n . . . . . . . . . . . . . . . . . . . . . . 93 3.3D.i2s troiBfbr uotwMinooitna.i n o .n . . .9 5. . . . . . . . . . . . . . . 3.3F.i3l trBartoiwoMnnoi taf.ino o r.n . . .9 7. . . . . . . . . . . . . . . . 3.3M.a4r tiPnrgoapfleoBerrr t oyw Mnoita.in o .n . 9.8 . . . . . . . . 3.Q4u adVraiaratti.ic o .n . . . . . .9 .8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14 F.irstV-aiOrart.di eo.rn . . . . .9 9. . . . . . . . . . . . . . . . . . . . . . . 3.4Q.u2a dVrraaitai.tci. o.n. . . . . . .1.0.1. . . . . . . . . . . . . . . . . . . 3.4V.ol3a toiGfle iotmyBe rtorwiMncoi ta.in.o n. . .10.6. . . . . . . 3.M5a rPkroovp .e.r.ty. . . . . . . . . .1.0.7. . . . . . . . . . . . . . . . . . . . . . . . . 3.F6i PrassstTa igmeDe i str.i.b.ut.i.o.n. . .1.0.8 . . . . . . . . . . . . . . . . 3.R7e flePcrtiino.cn.i .pl.e. . . . . . . .1.1.1. . . . . . . . . . . . . . . . . . . . . . . . 3.17 R.eflectio.n. .E.qu.a.l.i.ty. . .11.1. . . . . . . . . . . . . . . . . . . . 3.7F.i2Pr assstTa igmeDe i str.i.b.ut.i.o.n. 1.1.2. . . . . . . . . . . . 3.7D.i3s troiBfbr uotwMinooitnaai nnoI dntM sax im.u.m1 .13. 3.S8u mm.a.ry. . . . . . . . . . . . .1.1.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.N9o tes 116 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.E1x0e r.c.is.e.s. . . . . . . . . . .1.1.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . StochaCsatliccu. l.us. . . . . . . . . . .1.2.5. . . . . . . . . . . . . . . . . . . . . . . . . 4 41. Intro.d.uc.t.i.o.n . . . . . . . .1.2.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 InIttfeoog'Srrsi a mIlpn ltee g.r.a.n.ds. . . .1.2.5. . . . . . . . . . . . . . 4.12 C.onstortfueh c tIino.tne. g.r.a.l . . .1.2.6 . . . . . . . . . . . . . . 4.2P.r2o poetfrh tIein et.se g.r.a.l . . . . .1.2.8 . . . . . . . . . . . . . . . . 4.I3t' Iosn tfeogGrre anlIe nrtaelg .r.a.n.ds. . . .1.32. . . . . . . . . . . . . . 4.l4t O-DForoembu.ll.ia.n . . . . . . . . .1.3.7. . . . . . . . . . . . . . . . . . . . . . . 44..F1o rmfuoBlrra o wMnoita.in.o n. . . . . .1.37. . . . . . . . . . . . . . 4.4F.ro2m ufloIartP or oc.e.s.se.s. . . . .1.34 . . . . . . . . . . . . . . . . . 4.4E.x3a m.pl.e.s. . . . . . . . . .1.4.7 . . . . . . . . . . . . . . . . . . . . . . . . . 4.B5l ack-ScEhqoulae.ts.i-o.Mne. r.t.o.n . .1.5.3 . . . . . . . . . . . . . . . . 4.15 .EvoolPfuo tritVofanol. lu.ieo. . . . . .1.45 . . . . . . . . . . . . . . . 4.5E.v2o louOftp iotonin V.a.l.ue. . . . . .15.5. . . . . . . . . . . . . . . . 4.5E.q3u atthEievn ogl .ut.i.o.n.s . . . .1.65. . . . . . . . . . . . . . . . . . 4.5S.o4l utttoih Boeln a ck-Schole.s.-.M1.e5r.8t .o.n. E quation 4.5T.hG5er e.e.ks. . . . . . . . . . .19.5 . . . . . . . . . . . . . . . . . . . . . . . . . 4.5P.u6tl -PlCa ar.i.ty. . . . . . . . . 1.6.2. . . . . . . . . . . . . . . . . . . . . . 4.M6u ltiSvatroicaChbaaslltec.i uc.l .u.s . . . . .146. . . . . . . . . . . . . . . . . 4.16 M.ultBirpolwen ia.n. M.o.t.i.on.s. 1.6.4. . . . . . . . . . . . . . . 4.6I.t2O -DFooerbmfluoMilruna l tPirpolc.ee .ss.e.1s.5 6 . . . . . . 4.6R.e3c oganB irzoiwMnnogit a.in.o n. . . . .1.6.8. . . . . . . . . . . . 47. B rowBnriia.dn.g e. . . . . . . . . . .1.27 . . . . . . . . . . . . . . . . . . . . . . . . . . 47.1. GausPsrioac.ne .ss.e.s. . . . . . .127. . . . . . . . . . . . . . . . . . . . . 47.. B2r owBnriiaasdn gG aea usPsrioa.cne.. s..s. . .157. . . . . .

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