ܢௐܢಃ֥ࡎᆴܙ࠹47 ໓ᅣщݼ:1002 1566(2002)06 0047 03ܢௐܢಃ֥ࡎᆴܙ࠹ 杨春鹏1,吴国富2(1.ౝ֛ն࿐ࣁವ࿐ჽ,ౝ֛266071;2.ᇏݓ॓࿐ჽඔ࿐ა༢॓࿐࣮ჽႋႨඔ࿐࣮෮,Кࣘ10080)ᅋ ေ:本文利用股票的期权定价理论研究了我国股票市场上股票的配股权价值问题,并给出了具体的计算公式bܱՍ:配股权;期权;几何布朗运动ᇏٳোݼ:O212໓ངѓ്:A၂aႄ ၂Ϯ,ֹܢ൞ᆷഈ൧܄ඳᄝଖ၂ಒקರ௹ؓӻႵ܄ඳܢௐ֥ܢתοᅶ၂ק֥б২টؿྍ֥ܢௐbൌ࠽ഈᆺႵܢಃ֨࠺ರଽӻႵഈ൧܄ඳܢௐ֥ܢתҌႵಃ০ᄝࡼটଖ၂؍ൈࡗଽο၂ק֥б২ބࡎ۬ܓઙഈ൧܄ඳᄹؿ֥ྍܢௐbܢת෮ऎႵ֥ᆃᇕಃ৯ӫᆭູܢಃbܢ൞ഈ൧܄ඳᄝܢௐ൧ӆഈቋᇶေ֥ವሧٚൔ,ൈ,ൌീܢಃ္൞ሧᆀᄝܢௐ൧ӆഈࠆ౼ሧಃ֥၂ᇕٚൔbၹՎ,࣮ܢಃ֥ଽᄝࡎᆴܼؓնሧᆀ(Їওࠏܒሧᆀބಊഅ)ބഈ൧܄ඳႵሢགྷൌ֥ၩၬbՖݓܢௐ൧ӆ֥ൌ࠽ܢݖӱট,ु൮༵Ⴎഈ൧܄ඳ܄҃ܢყσ(ܢб২ބܢࡎ)۬,ᄜࣜݖܢתն߶ษં๙ݖ,ᆣࡓ߶ሙᆭ,ު൙߶ॖၛᄝᆷק֥Б़܄҃ܢࡎ۬ބб২,ѩಒקܢಃ֨࠺ರބቋުࢌॻರbൌ࠽ഈ,Ֆਸ਼ຓ၂۱࢘؇,ुܢಃ൞ܢಃ֨࠺ರଽӻႵഈ൧܄ඳܢௐܢת֥၂ᇕಃ০b၂Ϯ,ֹ۴ऌഈ൧܄ඳܢௐࡎ֥۬эሑঃ,ܢת࠻ॖၛൌീᆃᇕܢಃ္ॖၛ٢ఙᆃᇕܢಃ,ၹՎܢಃऎႵुᅨ௹ಃ֥ྟᇉ,൞၂ᇕ٤ѓሙ֥ुᅨ௹ಃbႮᇷ֥Black-Scholes௹ಃקࡎ܄ൔॖၛᆩ֡௹ಃࡎᆴ֥նཬ၇ঠႿᆳྛࡎ۬aܢௐԚࡎ۬ࠣ௹ಃ֥Ⴕིൈࡗ,ၹՎܢࡎ֥֮ۚaܢб২֥նཬބܢ֥௹ཋ႕ཙሢܢಃ֥ଽᄝࡎᆴbЧ໓ၩᆻ০Ⴈ௹ಃקࡎંট࣮ܢಃ֥ଽᄝࡎᆴѩ۳ԛऎุ֥ਈ߄ଆbؽaݓܢௐ൧ӆᇏ֥ܢಃᄝݓܢௐ൧ӆᇏ,ܢௐൌ࠽ܢಃ֥ࡎᆴູݣಃܢࡎაԢಃܢࡎᆭࡗ֥ҵحbࡌഡܢಃ֨࠺ರܢௐ൬ࡎູ۬P0,Ցರषࡎູ۬P1,ܢࡎູ۬Ph,ܢб২ູn(ᄝܢಃ֨࠺ರଽӻႵnܢܢௐުႵಃၛܢࡎ۬Phܓઙ1ܢܢௐ),ᄵܢಃ֥ࡎᆴູG1=P0-P1۴ऌݓܢௐ൧ӆഈܢௐ֥ൌ࠽ԢಃሑঃnP0+Ph,၂Ϯ:ֹP1=,ၹՎݓܢௐ൧ӆഈn+1ܢௐ֥ܢಃࡎᆴູnP0+PhP0-PhG1=P0-P1=P0-=n+1n+1 ൬۠ರ௹:2001-04-27
48ᇏ໓ނྏ௹़ ඔ࠹აܵ 21ज 6௹ 2002୍11ᄅ aܢಃࡎᆴ֥קࡎଆ༯૫ૌ০ႨBS௹ಃקࡎ܄ൔটܙܢಃ֥ଽᄝࡎᆴ,൮༵ૌ۳ԛBS௹ಃקࡎଆ,ࡌഡᆣಊ൧ӆഈೂ༯่ࡱӮ৫:1aᄍྸႨಆ҆෮֤છॢစളᆣಊ;2aીႵࢌၞٮႨࠇඥ൬;3a௹ಃ֥Ⴕི௹ଽીႵޣ০ᆦڱ;4a҂թᄝڄགส০ࠏ߶;5aᆣಊࢌၞ൞৵࿃֥;6aڄག০ੱrູӈඔؓ෮Ⴕ֞௹ರཌྷ;7aܢௐࡎ۬S࿖༯ඍࠫޅ҃ᄎdS= Sdt+ Sdz ఃᇏ: a ູӈඔ,ҕඔ ູֆ໊ൈࡗଽ(๙ӈࡌקູ1)୍ܢௐ֥ყ௹൬ၭੱ,ҕඔ ູܢௐࡎ֥۬ѯ,ੱdz൞၂۱Wienerݖӱ,dz= dt, ູѓሙᆞٳ҃(௹ຬູ0,ѓሙҵູ1֥ᆞٳ҃)bႮႿܢௐބཌྷႋ֥စളᆣಊ൳၂ࣁವ൧ӆ҂ಒקၹ֥႕ཙ,෮ၛBlackބScholes൮༵০Ⴈ҂ڱޣ০ܢௐބၛ҂ڱޣ০ܢௐູѓ֥ሧӁ֥စളᆣಊܒᄯ၂۱ڄགᆣಊቆކ,ಖުᄜ০Ⴈࡌഡ่ࡱ4֝ԛਔࠎႿ҂ڱޣ০ܢௐ֥ၩ၂ᇕစളᆣಊ֥ࡎ۬෮сྶડቀ֥ັٳٚӱ g g1+rS+ 2S2 2g t s2 S2=rg(1) ഈඍٚӱ(1)ࠧ൞٤ӈᇷ֥BSັٳٚӱb০Ⴈڄགᇏྟקࡎ,ંBlackބScholes֤ԛਔཌྷႋ൦ुᅨ௹ಃ֥קࡎଆg=-r(T-t)eE [max(ST-X,0)](2) ఃᇏ:E іൕڄགᇏྟൗࢸᇏ֥௹ຬᆴ,Xіൕ௹ಃ֥ᆳྛࡎ۬,Tіൕ௹ಃ֥֞௹ರb০Ⴈࠫޅ҃ᄎބؓඔᆞٳ֥҃၂ུห,ྟॖၛ֤ԛٚӱ(1)֥ࢳ༅іղൔ:ູg=SN(d1)-X-r(T-t)eN(d2)(3) ఃᇏln(S/X)+(r+ 2/2)(T-t):d1= T-td2=d1- T-tN(x)ູѓሙᆞٳ֥҃࠹ۀੱٳ҃ݦඔ(ࠧෛࠏэਈཬႿx֥ۀੱ)bႮႿܢб২ູn,ၹՎܢಃቔູ၂ᇕ௹ಃট,ुఃᆳྛࡎ۬ႋູ nP0+Ph=,ഡܢn+1ಃ֨࠺ರ֥ൈख़ູ0,ܢ֥࢚ॻႵི௹ཋູT,෮ၛ۴ऌBS௹ಃקࡎ܄ൔॖᆩܢಃ֥ଽᄝࡎᆴູnP+PG0h-rT2=P0N(K1)-eN(Kn+12)(4) ఃᇏln(P0/ )+(r+ 2/2)T:K1=,K2=K1- T T۴ऌڄགส০ࡌഡ,ႋႵ G1=G2(5)
ܢௐܢಃ֥ࡎᆴܙ࠹49Ⴎ܄ൔ(4)ॖᆩ,၂Ϯ౦ঃ༯(5)ൔѩ҂Ӯ৫b༯૫ૌটษ(ં5)ൔӮ৫่֥ࡱb֒ܢ֥࢚ॻႵི௹ཋTཟႿ0ൈ,K1ބK2ཟႿ౫ն,ၹՎN(K1)ބN(K2)ཟႿ1bᄜႮ܄ൔ(6)ॖᆩ,֒ܢ֥࢚ॻႵི௹ཋTཟႿ0ൈ,G2ཟႿP0-Ph=n+1G1,ࠧlimG=G1bT 20ႮႿᄝݓܢௐ൧ӆഈ֥ൌ࠽ܢ࢚ॻ௹ཋႵ၂؍ൈࡗ,෮ၛ၂Ϯ౦ঃ༯(5)ൔѩ҂Ӯ৫b༯૫ૌট࣮G1,G2ᆭࡗ֥նཬܱ༢,ູٚьૌᆺॉ੮ܢ֥၂۱ห൹౦,ྙࠧܢࡎ۬Ph=0(ܢ߄ູෂޣܢ֥౦ྙ),ః֥౦ঃษંোරb֒ܢࡎ۬Ph=0ൈ,PPG001=;G[(n+1)N(Kn+12=-n-rTeN(Kn+1)12)] ෮ၛေбࢠG1,G2ᆭࡗ֥նཬ,ᆺླ࣮ =(n+1)N(K1)-n-rTeN(K2)ა1ᆭࡗ֥նཬܱ༢,֒ >1ൈ,G1<G2;֒ <1ൈ,G1>G2;֒ =1ൈ,G1=G2b২ೂ:۳קN(K-rTP01)=;eN(K2)=,G2=n+1(+),֒n>2ൈ,G1<G2;֒n<2ൈ,G1>G2;֒n=2ൈ,G1=G2,ႮՎॖၛुԛܢб২ؓG1,G2ᆭࡗնཬܱ༢႕ཙޓնbሸഈ෮ඍૌॖၛ֤ԛೂ༯ఓൕྟ֥ࢲ:ંݓܢௐ൧ӆഈ֥ܢಃࡎᆴႵॖି֮ܙࠇۚܙܢಃ֥ଽᄝࡎᆴb၂Ϯ,ֹ֒ܢб২nࢠնൈ,ܢௐ൧ӆ߶֮ܙܢಃ֥ଽᄝࡎᆴ,ཌྷّ,֒ܢб২nࢠཬൈ,ܢௐ൧ӆ߶ۚܙܢಃ֥ଽᄝࡎᆴbഈඍࢲંؓႿࠏܒሧᆀႵሢᇗေ֥ႋႨࡎᆴ,ႮႿࠏܒሧᆀሧࣁحࢠն,֒ܢௐࡎ֮۬Ⴟܢࡎ۬ൈ߶۳ࠏܒሧᆀᄯӮࢠնാ,ၹՎ,ᆞಒܙ࠹ܢಃ֥ଽᄝࡎᆴႵ০Ⴟࠏܒሧᆀᆞಒܙ࠹ҕაܢ෮૫ਢ֥ڄག,ၛ૧ԛགྷԢಃު֥ܢௐࡎ֮۬Ⴟܢࡎ֥۬ሑঃ۳ࠏܒሧᆀᄯӮమᄝാb[ҕॉ໓ང][1] Black,F.,Scholes,M.,Thepricingofoptionsandcorporateliabilities[J]..,1973,81,637-659.[2] Hull,J.,OptionsFuturesandOtherDerivatives.[M].Prentice-Hall,1997.[3] Karatzas,I.,Shrve,.,BrownianMotionandStochasticCalculus[M].Springer-VerlagNewYork,1988.[4] աჱ,ဗԽவ.௹ಃ֥ڄགᇏྟקࡎაڄགส০[J]. ඔਈࣜ࠶აඌࣜ࠶࣮ ,1998,(9).ValuationofstockallotmentrightYANGChun p1eng,WUGuo fu2(,QingdaoUniversity,Qingdao266071,China;,theChineseofAcademyofSciences,Beijing100080,China)Abstract:Inthispaper,weapproachedthevaluationofstockallotmentrightbyusingoption-basedtechnique,ob :Stockallotmentright;optiongeometric;brownianmotion
