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520079()JournalofEastChinaNormalUniversity(NaturalScience)No.5Sept.2007:1000-5641(2006)05-0089-03¤¤,(,200062):O211.6:A0,[1].,,.,.1S[1;2]:dS=¹Sdt+¾Sdz(¿);(1)z(¿)Gauss-Wiener,¹;¾.,g,[3]S(T)=Sexp[(r¡g¡12¾2)T+¾z(T)];(2)r,S,tTt¤,t;t¤.(2)TS(T)t,S0(T)=Sexp[(¡g¡12¾2)T+¾z(T)]:(3)h(2)nai=S[¿¡(n¡i)h];i=1;2;3;:::;n;(4)¿=t¤¡t,.h(3)nbi=S0[¿¡(n¡i)h]=Sexpf(¡g¡12¾2)[¿¡(n¡i)h]+¾z[¿¡(n¡i)h]g;i=1;2;3;:::;n:(5)PFDAA=er¿max[!DAA(n)¡!K0;0];(6):2006-10:(10671072);(04SG27);(20060269016):(1981{),,.:(1954{),,,.90()2007!(1,¡1),K,DAA(n)=nXi=1bi=n;K0=e¡r¿K:¿=t¤¡t=nh;¿,n!1,DAA(n)!CDAA(t;t¤),CDAA(t;t¤)=1t¤¡tZt¤tS0(T)dT:(7)PFCDAA=er¿max[!CDAA¡!K0;0]:(8)22.1(1)[4]AA(n)»=¸GA(n);(9)AA(n),GA(n)(4),»=,¸=1+E(º+º2);º=1=2Var(lna)=nXi=1nXj=1[ln(ai=aj)]2=(2n2):2.2(1)[3;5]Caa=!¸SAgaN(!da+!¾pTn)¡!Ke¡r¿N(!da);(10)da=fln(¸SK)+(r¡g¡¾22)T¹g=(¾pTn);Aga=expfr(T¹¡¿)¡gT¹+12¾2(Tn¡T¹)g,dn=fln(SK)+(r¡g¡¾22)T¹g=(¾pTn);T¹=¿¡h(n¡1)2;Tn=¿¡(n¡1)(4n+1)6nh:(11)2.1(5),Cd=!¸dSAdN(!dd+!¾pTn)¡!Ke¡r¿N(!dd);(12)Ad=expf¡gT¹+12¾2(Tn¡T¹)g;dd=[ln(S¸der¿=K)¡(g+¾2=2)T¹]=(¾pTn);(13)¸d=1+E(ºb+º2b);ºb=1=2Var(lnb)=nXi=1nXj=1[ln(bi=bj)]2=(2n2):(6)er¿(10),(5)(4).max[!DAA(n)¡!K0;0].(5)(10),Cd1=¸dAd1N(!dd+!¾pTn)¡!K0e¡r¿N(!dd);5,91Ad1=expf¡r¿¡gT¹+12¾2(Tn¡T¹)g.Cd=er¿Cd1.¸d.E[V(lnb)]=(n2¡1)h6[12(g+¾22)2h+1n¾2];(14)Var[V(lnb)]=(n2¡1)(3n2¡2)15n3(g+12¾2)2¾2h3;(15)¸d=1+1=2E[V(lnb)]+1=4fV[V(lnb)]+fE[V(lnb)]g2g:(16)2.2(2)Ccd=!S¸cde¡¿=2(g¡¾2=6)N(!dcd+!¾p¿=3)¡!Ke¡r¿N(!dcd);(17)¸cd=1+E(ºb+º2b)n!1¸d,dcd=[ln(S¸cder¿=K¡(g+¾2=2)¿=2]=(¾p¿=3):(12)n!1.3..,,.,,.4.,,.,1,.$100,$105,7%,3%,20%.,..!=1;S=100;K=105;r=0:07;g=0:03;n=12;h=1=12;¾=0:2:(11)T¹=0:542;Tn=0:376.(13)Ad=0:981;dd=¡0:048.(14){(16),E[V(lnb)]=E[V(lnb)]=0:0068;Var[V(lnb)]»=0;¸d=1:0034.(12)Cd=!¸dSAdN(!dd+!¾pTn)¡!Ke¡r¿N(!dd)=$5:05.,12,$2.2934,$3.2294,$3.9382,$4.5280,$5.0407,$5.4981,$5.9132,$6.2943,$6.6475,$6.9770,$7.2862,$7.5776,$65.2236.,.[][1]JORIONF.FinancialRiskManagerHandbook[M].2nded.London:JohnWiley&SonsInc,2003.[2]HULLJC.Options,Futures,andOtherDerivatives[M].,2001.[3]ZHANGPG.ExoticOptions[M].Singapore:WorldScience,1997.[4]MALLIARISAG,BrockWA.StochasticMethodsinEconomicsandFinance[M].Amsterdam:North-HollandPublishingCompany,1982.[5]MERTONR.Thetheoryofrationaloptionpricing[J].BellJournalofEconomicsandManagementScience,1973(4):141-183.