对数正态分布及其在证券中的应用

233Vol23No320129JournalofSuzhouVocationalUniversitySep2012215104.BS.LognormalDistributionanditsApplicationintheSecuritiesWANGZhi-gang(DepartmentofBasicEducationSuzhouVocationalUniversitySuzhou215104China)AbstractThepaperfirstintroduceslognormaldistributionandrelalionbeweenlognormaldistributionandnormaldistributionBecausethemovementofsecuritiespricesfollowslognormaldistributionthecharacteristicsofthelognormaldistributionisusedtopredictthestockpriceandthewithB-SoptionpricingmodelonthecalculationofthestockoptionpriceandthebasisofthegraspoftheinvestmentopportunitytoprovideanimportantreferenceKeywordslognormaldistributionestimatestockoptionprice1XY=lnXN(μσ2)Xμσ2Φ(y)φ(y)N(μσ2)Y=lnXN(μσ2)X=eYx0XFX(x)=P{Xx}=P{eYx}=P{Ylnx}=Φ(lnx)XxfX(x)=0(1979).X[1]Xμσ2dx=a(xt)dt+b(xt)dzdza(xt)b(xt)xtxab2G(xt)xtGdzBSrSdS=μSdt+σSdz(1)μμSσσSdzεt(1)S(2)TSTTStSTCSt(r)CBS2012323(3)XΦxA10020%15%95%A(2)lnST(4616(0058)2)95%lnST(45024730)ST(e4.502e4.730)9020ST11330A9020(95%)11330(95%)A1133090206848010%20%CS=84X=80rσTt.(3)C.6952952952μσμσ[1][M]2009132156[2][J]201111(5)811[3][M]201087100[4]DEGROOTMHSCHERVISHMJ[M]2005123149