有交易成本的期权定价方法Ξ

185(101)20009X,Black2Scholes,,,,,Black2Scholes,,70,201973,BlackScholes,BlackScholes,Black2Scholes(B2S)[1],,MertonCoxRossIngersoll,[2],,,,,,,[3],,,1,,,B2S,B2S,:(1);(2),;(3);(4)(S)(t)31X:1999-12-06:;:7100793(79670076),:dS=LSdt+RSdZ(1),L;R;dZWiener,:dZ=dt(2)(2),:f()=12Pe-122(3)ITO,(V(S,t)):dV=(LSV55S+12R2S252V5S+5V5t)dt+RS5V5SdZ(4)V(S,t)S(0):0=V-$S(5)dt(dt0),(1)(4),0:d0=RS(5V5S-$)dZ+(LS5V5S+12R2S2525S2+5V5t-L$s)dt(6)$,(6)dZ,:$=5V5S(7)(7)(6),:5V5t+rS5V5S+12R2S252V5S2=rV(8)r,(8)B2S,[4,5]TEC(S,t),:C(S,T)=max(S-E,0)(9)C(S,t):C(S,t)=SN(d1)-Ee-r(T-t)N(d2)(10),d1=ln(SöE)+(r+R2ö2)(T-t)RT-t,d2=d1-RT-t,N(õ)(P(S,t)):P(S,t)=C(S,t)-S+Ee-r(T-t)=Ee-r(T-t)N(-d2)-SN(-d1)(11)2,BlackScholes,($),,$,·,:C=52V5S2(12)·,$,$,·,$,·,,·,,·;,41,·,(11)(12),$·(1),S12)$·1$(5Vö5S)·(52Vö5S2)N(d1)N(d1)-1N(d1)SRT-t1$2·3,,,,(5)0,0Dt,:DS=LSDt+RSDt(13),,(K)X,(X0)(X0)ûXûS,KûXûS(13),Dt,0:D0=RS(5V5S-$)Dt+(LS5V5S+12R2S252V5S2+5V5t-LDS)Dt-KSûXû(14)(7),:$=5V5S(S,t)(15)Dt,Dt(Dt0),$:$=5V5S(S+DS,t+Dt)(16)$,,(15)(16),X:X=5V5S(S+DS,t+Dt)-5V5S(S,t)(17)Taylor,(16):515V5S(S+DS,t+Dt)=5V5S(S,t)+DS52V5S2(S,t)+Dt52V5S5t(S,t)+(18)(13),(16),:XDS52V5S2(S,t)52V5S2RSDt(19)(3),KûXûS:E(KSûXû)=2PKRS252V5S2Dt(20)(15)(14),D0:E(D0)=(5V5t+12R2S252V5S2-KRS22PDt52V5S2)Dt(21),:5V5t+12R2S252V5S2-KRS22PDt52V5S2+rS5V5S=rV(22)(22),,·,,·,:5V5t+12(R2-2KR2PDt)S252V5S2+rS5V5S=rV(23)(23)B2S,:Rd=R2-2KR2PDt(24),B2S,:Rd=R2+2KR2PDt(25)K=0,B2S(24)(25)R,,,,4,,,B2S,,,,1Black,Scholes.ThePricingofoptionsandCorporateLiabilities.JournalofPoliticalEconomy,1973,81(7):6376552[],..,1997,399447(22)61OptimalInsuranceCoverageforPortfoliosofRiskyInvestmentXuShaoxianAbstractThepaperexaminestheoptimalinsurancepolicesfromtheinvestor’spointview.Weusethemean2varianceapproachandthemulti2hazardriskmodeltoanalyzetheinfluenceofthespeculativeriskprofit,insurableriskloss,therateofreturnontherisk2freeassetandthepremiumrateontheoptimaldecision.Ourresultsprovideareliabletheorybaseformodernfirmtomakeoptimalinsurancestrategies.Byincorporatingtherisk2freeassetintotheanalysis,wemaygainconsiderableinsight.Fromtheinsured’spointview,insuranceinstrumentcomputewiththerisk2freeinvestmentsintheportfoliosaswellasotherinvestmentsintheportfoliosasmeansofriskreduction.Keywordsoptimalinsurance,mean2varianceutility,therisk2freeasset,insurablerisk,portfolios(16)3GuyBarles,HalilMete.OptionpricingwithtransactioncostsandanonlinearBlack2Scholesequation.JournalStochast,1998,72(2):3693974..,1982,58655PoulWilmott,SamHowynne.TheMathematicsofFinancialDerivatives.CambridgeniversityPress,1995,5867AMethodofOptionPricingwithTransactionCostsZhengXiaoyingChenJinxianAbstractBaseduponunderlyingasset’slognormaldistributionandhedgingcontinuously,Black2ScholesmodelhassolvedEuropeanoption’spricinginefficientmarketsuccessfully.Nevertheless,theinvestorsinrealfinancialmarkethavetofacealotoftransactioncosts.Onthedefinitionoftransactioncosts,nonlinearoptionpricingmodelispresentedundertheconditionofdiscretetradingtimes.ThelongpricingofEuropeanoptionandtheshortpricingofthatarediscussedalso.KeywordsTransactioncosts,Black2Scholesmodel,Portfolio,Non2arbitrarytheorem22