基于激励机制的美式股票期权相对多指数化模型设计

200755:100026788(2007)0520029206,,(,410083):,,,.,Delta,,.:;;;:F06215:ADesignofAmerican2styleStockOptionRelativeMulti2indexModelbasedonIncentiveMechanismHUANGJian2bai,YINZhi2yuan,ZHONGMei2rui(SchoolofBusinessofCentralSouthUniversity,Changsha410083,China)Abstract:Basedonconsideringthetraditionalstockoptionsdeficiency,thethoughtofEuropean2stylestockoptionmulti2indexandtherelativedesignintegratedwithAmerican2stylestockoptioncharacteristicisadoptedtoconstructAmerican2stylerelativemulti2indexstockoptionagreementpriceandpricemodelinthispaper,accordinglyincentivecontractofAmerican2stylerelativemulti2indexstockoptionisdesigned.BasedonstaticcomparativeanalysisofthepricemodelandcontrastanalysisbetweenEuropean2styleandAmerican2stylerelativemulti2indexstockoptioninthepricemodel,aconclusionisdrawn.ItisthatDeltacoefficientofAmerican2stylerelativemulti2indexstockoptionisbiggerthanEuropean2stylerelativemulti2indexstockoptionandtheuncertaintyquestionofincentiveismorecomprehensiveconsideredinAmerican2stylerelativemulti2indexstockoption.Asaresult,theincentiveefficiencyismoreeffective.Keywords:multi2index;relatively;theEuropean2stylestockoption;theAmerican2stylestockoption:2006201220:(70672106);(104260);(0403019):(1954-),(),,,,;(1983-),(),,,;(1978-),(),,,.1,..,,,.,().,,,,,.,.2211.,.Mirrlees(1974,1976)[1,2],Holmstrom&Milgrom(1987)[3],,.GibbonsMurphy(1990)[4]1974198610491668CEO,CEO,.,Rappaprot(1999)[5].Johonson&Tian(2000)[6]Margrable2Fisher2Stulz(1978)[7],,.(2002)[8]Johonson&Tian.ShaneA.Johson(2004)[9],,,,.Jin2ChuanDuan&JasonWei(2003)[10],,,,.(2005)[11],,.,.,,PeterLochteJorgensen(2002)[12],,deltadelta,.,,,.212Johson&Tian(2000),S(t)I(t):dS(t)PS(t)=(S-S)dt+SdWS(t),(1)dI(t)PI(t)=(I-I)dt+IdWI(t),(2)dWS(t)dWI(t)=dt,(3)S,SS,;I,IS;WS(t)WI(t),.Johson&Tian(2000):S=r+(I-r),(4)=CovdS(t)S(t),dI(t)I(t)VardI(t)I(t)=SIdt2Idt=SI.(5)P.LochteJorgensen(2001),t:H(t)=S(0)(I(t)PI(0))e(g+)t,(6),=(r-S)-(r-I)+SI(1-)P2,r.(),.,E(0)[S0320075(0)PI(0)]=H(0),=S-r-(I-r),.:S(0)=H(0),=1;1,1.:max[S(T)-H(T),0].,Margrabe(1978),t:C(t)(A)=e-S(T-t)[S(t)N(d1(t))-H(t)N(d2(t))]+Tt(N(dI(t,u))SS(t)e-S(u-t)+(g-S)H(t)e(g-S)(u-t)N(N2(t,u)))du,(7)N(),:d1(t)=lnS(t)H(t)+-g+122x(T-t)(xT-t),(8)d2(t)=lnS(t)H(t)+-g-122x(T-t)(xT-t),(9)d1(t,u)=lnX3(u)X(u)+S-g+122x(u-t)xu-t,(10)d2(t,u)=lnX3(u)X(u)+S-g-122x(u-t)xu-t,(11)x=X1-2.(12)(7),,x,Ht.,x.,S(t)H(t)X,,.3311L,LP.,P,L-1.,.,LP:dS(t)PS(t)=(r-S+2S)dt+SdWQS(t),(13)dIi(t)PIi(t)=(r-Ii+IiS)dt+IidWQIi(t),(14)dWQS(t)=dWS(t)+Sdt,(15)dWQIi(t)=dWIi(t)+Iidt,(16)S=S-r-2SPS,(17)Ii=Ii-r-IiSPIi,(18)dWQi(t)dWQj(t)=i,jdt,(i,j=0,1,2,,P)(19)WQi(t)Q,S(t),Ii(t)ti.i,i,i,jdWQi(t)dWQj(t).:i,j=1,i=j;i,j1,ij.(20)135X0(t)=ln[S(t)PS(0)]Pt,(21)Xi(t)=ln[Ii(t)PIi(0)]Pt;i=1,2,,P,(22)xi(t)[0,t],X(t)P1:X(t)=[x0(t),x1(t),x2(t),,xP(t)]T;X(t)tLtV,:L=[l0,l1,l2,,lP];li=r-i-2iP2;i=0,1,2,,P,(23)V=[2i,j]i=0,1,2,,Pj=0,1,2,,P;i,j=i,jij;i,j=1,2,,P.(24):=(S-r)-Pi=1i(Ii-r),(25)iIiP(l0,l1,l2,,lP).V,,i:=[1,2,,P]T=V-1P,=[21x,22x,,2Px];VP=[2i,j]i=0,1,2,,Pj=0,1,2,,P,(26)Holmstrom(1982),,.(13)(19),,.,:E[S(t)|Ii(t);i=1,2,,P;=0].(27),x0(t)x0(t),x1(t),x2(t),,xP(t):€l0=l0+TV-1P(x(t)-L),€20=20-TV-1P,(28)x0(t),:S(t)=S(0)etx0(t).S(t)xi(t),,:E[S(t)|Ii(t);i=1,2,,P]=S(0)e[€l0+€20P2]t,(29),:E[S(t)|Ii(t);i=1,2,,P]=S(0)Pi=1[Ii(T)PIi(0)]ie(+)t,(30)=(r-S)-Pi=1i(r-Ii)+12Pi=1(2i-2i0)i.(=0),.,:E[S(t)|Ii(t);i=1,2,,P;=0]=S(0)Pi=1[Ii(T)PIi(0)]iet.(31),g,=1,1,1;g0.t:H(t)=S(0)Pi=1[Ii(T)PIi(0)]ie(g+)t.(32)312Margrabe(1978),Ito:dH(t)H(t)=Pi=1[(g+r-S+2i2Ii)dt+iIidWQIi(t)],(33)t:C(t)(A)=e-S(T-t)[S(t)N(d1(t))-HtN(d2(t))]+2320075Tt(N(d1(t,u))SS(t)e-S(u-t)+(g-S)H(t)e(g-S)(u-t)N(N2(t,u)))du,(34)N(),:d1(t)=lnS(t)H(t)+-g+122(T-t)(xT-t),(35)d2(t)=lnS(t)H(t)+-g-122(T-t)(T-t),(36)d1(t,u)=lnX3(u)X(u)+S-g+122(u-t)(u-t),(37)d2(t,u)=lnX3(u)X(u)+S-g-122(u-t)(u-t),(38)2=Pi=12ixi.(39)313,.,.,:H(0)e(r-S)Tmax[S(T)PH(T)-1,0],H(0)=S(0)H(0)e(r-S)T.,S(T)PH(T),.T,e(r-S)T,.T:C(t)(R)=H(0)ert-STS(t)H(t)N(d1(t))-N(d2(t))+1H(t)Tt(N(d1(t,u))SS(t)e-S(u-t)+(g-S)H(t)e(g-S)(u-t)N(N2(t,u)))du,(40)N(),:d1(t)=lnS(t)H(t)+-g+122(T-t)(xT-t),(41)d2(t)=lnS(t)H(t)+-g-122(T-t)(T-t),(42)d1(t,u)=lnX3(u)X(u)+S-g+122(u-t)(u-t),(43)d2(t,u)=lnX3(u)X(u)+S-g-122(u-t)(u-t),(44)2=Pi=12ixi,(45)d1(t)d2(t).:C(t)(R)=H(0)e(r-S)tH(t)C(t)(A).(46).,,H(t).,.I(t)0,..4411335,,,,,.,:(S(t),H(t))A5C(t)(A)5S(t)=e-S(T-t)N(d1(t))+TtN(d1(t,u))Se-S(T-t)+n(d1(t,u))u-t(Se-S(T-t)+(g-S)x3(u)eSt)du.(47)(46),:(S(t),H(t))R5C(t)(R)5S(t)=H(0)e(r-S)tH(t)5C(t)(A)5S(t)=(S(t),H(t))AH(0)e(r-S)tH(t).(48)412(46),H(0)ert-STS(t)H(t)N(d1(t))-N(d2(t)),,,S(t)PH(t),:H(0)ert-STH(t)Tt(N(d1(t,u))SS(t)e-S(u-t)+(g-S)H(t)e(g-S)(u-t)N(N2(t,u)))du,(49)(49),.,S(t)PH(t),,,(49),,,,.:T=10,g=0,1=013,S=0105,2=014,r=01041delta413,,(2005).(48),deltadelta(1),.,,,.,,.5,,.,.:,,.,Delta,.,,.,.(54)4320075[3]CochraneJH.AssetPricing[M].Princeton:PrincetonUniversityPress,2001.[4].[M].:,2004.ShiSZ.TenPresentationsofFinancialEconometics[M].Shanghai:ShanghaiDometicPublishing,2004.[5]EmmerS,KlppelbergC.OptimalportfolioswhenstockpricesfollowanexponentialLvyprocess[J].FinanceStochast,2004,8:17-44.[6]FujiwaraT,MiyaharaM.Theminimalent