ֻ12जֻ4௹ܵ ॓ ࿐ ࿐ Б 2009୍8ᄅ JOURNALOFMANAGEMENTSCIENCESINCH ॖඁ߭ॖሇߐ์གྷᅏಊປಆҷࢳקࡎم 周其源1,2,吴冲锋1,刘海龙1(1.ഈݚࢌ๙ն࿐νࣜ࠶აܵ࿐ჽࣁವ۽ӱ࣮ᇏྏ,ഈݚ200052;2.လሧӁܵႵཋ܄ඳ,ഈݚ200120)ᅋေ:在Black Scholes期权模型假设框架下,依据风险中性定价原理,采用完全拆解法,将可赎回可转换贴现债券完全拆解为以下5种简单证券的组合:一种与之对应的普通贴现债券,两种立即支付型规则美式二值买权a一种规则上敲出买权和一种延迟支付型规则美式二值买权,并据之推导出定价解析式.不仅为认知其价值组成提供了全新视角,而且相对现有数值定价法,该解析式大大提高定价效率.ܱՍ:可赎回可转换贴现债券;完全拆解法;上敲出买权;美式二值买权;衍生证券定价ᇏٳোݼ:F224;C931 ໓ངѓ്:A ໓ᅣщݼ:1007-9807(2009)04-0135-100 ႄ ࢸ่ࡱݖႿگᄖ,ૌ҂֤҂ҐႨႵཋҵٳمࢳ.N[3]yborgቋᄪᄍྸᅏ༏ੱڜބթᄝۚࠩᅏ۴ऌࢌၞ෮࠹ඔऌ,ሱ2003୍ၛট,ؿྛಊ.൙ൌഈ,০ੱЧദ္൞ൈэ֥,ູՎ,Brennanॖሇߐᅏಊ(ሇᅏ)ၘࣜӮູᇏݓഈ൧܄ඳᄜವބ4]Schw[artz๙ݖႄೆVasicek০ੱଆ[5],ቋᄪሧ֥ᇶေ౻֡ᆭ၂.ႮႿሇᅏ൞၂ᇕൈടࠣᅏิԛਔᄝંഈ۷ࡆކ֥ࠎႿ܄ඳࡎᆴބ০ੱಊaܢௐބ௹ಃ֥گᄖࠁކစളᆣಊ,ູఃקࡎ֥ਆၹሰส০קࡎଆ.ෛ,ު۷؟࿐ᆀҐႨਔٳگᄖ:1)ሇᅏᄝЧᇉഈ൞ᄝᅏಊࠎԤഈଽݣ؟۷ູކ֥০ੱଆটսูVasicek০ੱଆ,ᇕܢௐ௹ಃ,Чദ࠻ऎᅏ,ྟႻऎܢ,ྟطෛሢೂC[6]arayannopoulosҐႨCIR০ੱଆ[7],Lvovѓ֥ܢࡎэ߄طՎཨдӉ;2)ሇᅏ෮ଽݣ֥؟ᇕ֩[8]ҐႨHW০ੱଆ[9].ܢௐ௹ಃᆭࡗཌྷቔႨ,ѩ҂ି৫षট,҂ିᆰഈඍࠎႿ܄ඳࡎᆴ֥ส০קࡎଆ,࣐ܵࢤႋႨBlack Scholes௹ಃקࡎ܄ൔ.࣐ܵೂՎ,ॖሇߐᅏಊקࡎ໙,ีᄝЧᇉഈಯᄝંഈડቀሱദ၂ᇁྟ,ޓ൞ކ.ಖط,ᄝൌಖඋႿส০קࡎં֥ႋႨٓԐᇏ,ᆃུଆ֥ॖҠቔྟޓҵ,ᆃ൞ၹ:ູѩ٤.1977୍,܄ඳ෮ႵሧӁ൞ॖࢌၞ֥,ၛᇁޓܙ࠹܄ඳ[1]Ingersollቋᄪࡼส০קࡎંႋႨ֞ཌྷؓࡥֆ֥٤ඁ߭ॖሇߐᅏಊބॖඁ߭ॖሇߐ์གྷᅏಊࡎᆴࠣఃѯੱ֩ཌྷܱҕඔ.ູՎ,McConnellބ[10]֥קࡎ໙,ีิԛਔᄝંഈࢠູކ֥ࠎႿ܄Schwartzิԛਔ۷ऎൌႨྟ֥ࠎႿѓ֥ܢࡎ֥ඳࡎᆴ֥ֆၹሰส০קࡎଆ.ᄝھࠎԤഈ֥ֆၹሰส০קࡎଆ.ಖط,֒ၛѓ֥ܢௐቔູު࿃࣮,ࠇᆀ٢ॺఃభิࡌഡ,ࠇᆀॉ੮۷؟ሇѓ֥ሧӁൈ,ႮႿܢࡎ҂ॖିູڵ,ᆃࣼஆԢਔໃᅏ่ॻ֞௹Ӂބ֞௹ິჿ֥ॖି.ྟູਔҀᆃ၂ಌ,ࠇᆀॉ੮۷؟ڄགၹሰ.২ೂ,BrennanބSchw[2]artzቋᄪᄍྸթᄝܢ০aᅏ༏aཊ,ૌ҂֤҂ҐႨᄝંഈѩ҂ିડቀሱദ၂ඁ߭႗ჿඏ่ࡱၛࠣሇߐࡎ۬э߄,ಖط,ႮႿшᇁྟ֥ྐႨ০ҵم.ෛ[11],ުTsiveriotisބFernandes ൬۠ರ௹:2005-09-28;ྩרರ௹:2007-03-20.ࠎࣁཛଢ:ݓࡅሱಖ॓࿐ࠎࣁሧᇹཛଢ(70671068).ቔᆀࡥࢺ:ᇛఃჷ(1975 ),ଳ,תށᄶದ,Ѱൖ.Emai:lqiyuanzhousun@
136 ܵ ॓ ࿐ ࿐ Б2009୍8ᄅ০Ⴈࡎᆴٳࢳمննࢆ֮ਔྐႨ০ҵم෮֝ᇁ֥ሱദ҂၂ᇁྟ.ဢֹ,ູਔ࡙ܤ০ੱ֥ൈэྟ,1 קࡎࢳ༅ൔ࣮གྷሑY[12]igitbasiogluҐႨCIR০ੱଆิԛਔࠎႿѓ֥ܢࡎބ০ੱ֥ਆၹሰส০קࡎଆ.ෛު,ॖၛϜܱႿሇᅏקࡎࢳ༅ൔ֥ᇶေ໓ངູ݂D[13][14]avisބLischka,Barone Adesi֩ᄵҐႨਔਆো.၂ো൞ᆰࢤࢳ෮ࡹส০קࡎଆ.۷ູކ֥[1]HW০ੱଆ.Ingersollቋᄪ၇ऌࠎႿ܄ඳࡎᆴ֥ֆၹሰสൌᆣіૼ,ೂK[15]angބLeeၛࠣHam০ଆ,ࠆ֤҂ᆦڱܢ০౦ঃ༯٤ඁ߭ॖሇߐ์ilton֩[16],ᄝູॖሇߐᅏಊקࡎൈ,္сྶൈॉ੮གྷᅏಊބCCDB֥קࡎࢳ༅ൔ.ᄝఃࠎԤഈ,ఃྐႨڄགN[3]yborg๙ݖࡌק܄ඳࡎᆴႮڄགሧӁބڄག.࣐ܵҐႨ[11]TsiveriotisބFernandes෮ิԛ֥ࡎᆴٳࢳمॖၛཁᇷࢆ֮ྐႨ০ҵم෮ሧӁਆ҆ٳቆӮ,ٳљࠆ֤ᆦڱᅏ༏ࠇթᄝܢ০֝ᇁ֥ሱദ҂၂ᇁ,ྟಖط,ྐႨ০ҵЧദᆺ൞ᄝൈ٤ඁ߭ॖሇߐᅏಊ֥קࡎࢳ༅ൔ.ಖط,ૌൌ࠽൧ӆᇏᆰࢤܴҳ֥֞၂۱ඔᆴ,ၛᆭטᆜ์൞ၛ܄ඳࡎᆴቔູѓ֥ሧӁ,ႮႿၛܙ࠹܄ඳགྷੱࡎᆴѯੱ֩ҕඔ,ᆃུࢳ༅ൔၛൌ࠽ႋႨ.,ᄝંഈѩކࢳ;Վຓ,ྐႨ০ҵЧദ္൞ൈэ֥,ၛܙ࠹.ູՎਸ਼၂ো൞,๙ݖ࣍රҷࢳمࠆ౼࣍රקࡎࢳ,Davisބ[13༅ൔ].ᄪ௹,ೂBaum[19ol֩ᆰࢤࡼ٤ඁ߭ॖሇߐ]Lischka,ၛࠣAyache֩[17],ҐႨ۷ູކ֥ࡥൔٚمᅏಊࡥֆֹ࣍රҷࢳູՂᅏಊބၛھՂᅏಊࡎᆴ(reduced formapproach)ॉ੮ఃྐႨڄག,ᄝંഈ۳ԛਔ۷ູކ֥ࠎႿܢࡎ֥ֆၹູᆳྛࡎ֥۬ൔઙಃ,ࠇᆀҷࢳູ෮ିܔሇߐሰส০קࡎଆ.ᄝఃࠎԤഈ֥ཌྷႋඔਈ֥ܢௐބၛؓႋՂᅏಊࡎᆴູᆳྛࡎ,Yigitbasiogluބ֥۬ൔછಃ.ਟၬཌྷ֩[20]ࡼॖඁ߭ॖሇߐᅏಊA[18]lexander๙ݖႄೆCIR০ੱଆ,Ⴛࡼᆭঔᅚ࣍රҷࢳູ3ᇕᆣಊ:Ղᅏಊ,ሧᆀႚႵ֥ၛሇູࠎႿܢࡎބ০ੱ֥ਆၹሰส০קࡎଆ.ߐࡎູ۬ᆳྛࡎ֥۬ሇߐಃ(ૅൔઙಃ)ބؿྛሸഈ,ሇᅏקࡎଆၘࣜؿᅚ֤ཌྷ֒ປ,ఃᆀႚႵ֥ၛඁ߭Ԩؿࡎູ۬ᆳྛࡎ֥۬ඁ߭ಃनקࡎ༂ҵၘࣜॖၛФ॥ᇅᄝ5%ၛ༯(ૅൔઙಃ).ಖط,ૌϜሇߐಃაඁ߭ಃुቔ(B]arone A[14desi֩).ಖط,ູਔࢳഈඍଆ,ཌྷ৫֥௴๙ܢௐ௹ಃ,ᄝંഈ,ޭਔૌсྶႨ֞ႵཋҵٳمaMonteCarloଆمࠇႵཋᆭࡗ֥ཌྷቔႨ.০Ⴈؽҭඎקࡎم,Hoބჭم֩ࢠູگᄖ֥ඔᆴٚم.ᄝට༏ຣэ֥֒భ[21]Pfefferൌᆣіૼ,ᄝଖུ౦ঃ༯,ᆃᇕޭࡼ֝ൈս,ᆃུٚم֥קࡎིੱഉႵրิۚ.Վຓ,ᆃᇁࢠնקࡎொҵ,൞҂ॖ౼֥.ུקࡎଆໃି۳ԛॖඁ߭ॖሇߐ์གྷᅏಊ֥ࠎЧࡎᆴቆӮ.2 ປಆҷࢳمູՎ,Ч໓ಪູ,ࣼᇏݓሧᆀಕุؓሇᅏࡎᆴ֥ಪᆩགྷሑط,ቋݺିܔࡼሇᅏᆃ၂گᄖࠁ ॖඁ߭ॖሇߐ์གྷᅏಊކစളᆣಊປಆҷࢳູၞႿࢳ֥؟ᇕཌྷؓࡥֆᄝݓଽຓൌ࠽ሇᅏ൧ӆᇏ,Ⴕሢ؟ᇕ؟ဢ֥ᆣಊ֥ቆކ,ൈ,ቋݺିܔࠆ֤ၞႿҠቔ֥קࡎॖሇߐᅏಊ.Ч໓࿊ᄴཌྷؓࠎԤ֥٤߭൲ॖඁ߭ࢳ༅ൔ,ࣼཞBlack Scholes௹ಃקࡎ܄ൔ.ᄝᆃ၂ॖሇߐ์གྷᅏಊቔູ࣮ؓའ.ႮႿః่ॻЧദනਫ਼༯,Ч໓ၛཌྷؓࠎԤ֥ॖඁ߭ॖሇߐ์གྷᅏ္ॖၛႵэ߄,ູਔࡥ߄໙,ีࢣൕఃࠎЧࡎᆴಊ(CCDB,callableconvertiblediscountbonds)ቔູቆӮ,Ч໓ࡼఃऎุ่ॻཋקູၛ༯౦ঃ.(D1)࣮ؓའ,ᆌؓၛສҷࢳٚم҂ܔປಆ,ၛᇁ༂ҵܱႿሇߐ่ॻ: ᄝః௹ཋଽ,ӻႵᆀႵಃᄝၩࢠն֥ಌ,ׄሇэҷࢳනਫ਼,҂ᄜၛ௴๙௹ಃ,طൈख़οᅶყ༵ഡק֥ሇߐࡎ۬ᆳྛሇߐಃ.!ః൞ၛఅၳ௹ಃ(exoticoptions)টҷࢳ.ቋᇔ,ࡼሇߐࡎ۬ޚק.(D2)ܱႿඁ่߭ॻ: ᆺႵ֒ѓCCDBປಆҷࢳູ5ᇕཌྷؓࡥֆᆣಊ֥ቆކ.ᆃ֥ܢࡎഈᅨ֞ყ༵ഡק֥ඁ߭Ԩؿࡎ۬ၛഈൈ,ປಆҷࢳ҂ࣇູಪᆩఃࡎᆴቆӮิ܂ਔಆྍ൪ؿྛᆀҌႵಃοᅶყ༵ჿק֥ඁ߭ࡎ۬ᆳྛඁ߭࢘,طऌՎॖၛ֝ԛఃקࡎࢳ༅ൔ.ಃ,ࠧթᄝཌྷؓࡥֆ֥ೈඁ߭ჿඏ่ࡱ.!ఃඁ߭
ֻ4௹ᇛఃჷ֩:ॖඁ߭ॖሇߐ์གྷᅏಊປಆҷࢳקࡎم 137 ࡎ۬ޚק[1].∀ඁ߭๙ᆩ௹,Ingersoll္֩ࣉྛ:ູؿྛᆀႚႵ֥aᅰθඣູP2aܥקᆦڱحູਔೂՎཋק.࣐ܵᄝൌ࠽൧ӆᇏॖඁ߭ॖሇߐ์BF֥ӾᆦڱܿᄵૅൔؽᆴઙಃABCd(S0,T;གྷᅏಊ၂ϮႵሢඁ߭๙ᆩ௹,ಖط,ඁ߭๙ᆩ௹BF),ሧᆀႚႵ֥aᅰθඣູP2aܥקᆦڱحؓॖඁ߭ॖሇߐ์གྷᅏಊંࡎᆴ֥႕ཙࢠཬ,ູBF֥৫ࠧᆦڱܿᄵૅൔؽᆴઙಃABCi(S0,ೂՎཋק൞ࠎЧކ֥.২ೂ:֒ѓ֥ܢࡎղ֞ࠇT;BF)ބሧᆀႚႵ֥ؓႋ์གྷᅏಊDB(S0,T).ӑݖሇߐࡎ۬130%ൈ,ؿྛᆀႵಃοᅶሇᅏ૫ᄝഈඍҷࢳݖӱᇏ,ႮႿҐႨࡼࡥֆᆣಊՖᆴ֥105%ᆳྛඁ߭ಃ.ࡌקఃሇߐࡎູ۬10CCDBᇏᇯ۱Љ֥ٚم,Ֆطᄝ൬ၭหྟഈ,҂ჭ,ః૫ᆴູ100ჭ,ପહᆺႵ֒ѓ֥ܢࡎղ֞ࠇࣇᆃ5ᇕࡥֆᆣಊᆭࡗીႵޅᇗן,طՖӑݖ10#130%=13ჭൈ,ؿྛᆀҌႵಃ࿆ۡοCCDBᇏᇯ۱Љᆃ5ᇕࡥֆᆣಊᆭު,္ીႵᅶ105ჭ֥ሇᅏඁ߭ࡎ۬ᆳྛඁ߭ಃ.(D3)ܱႿޅഺჅ,ၹՎھҷࢳ൞ؓCCDB֥∃ປಆҷࢳ%.ః่ॻ:ીႵ෭ק௹่ॻa߭൲่ॻaᇗᇂ่ॻ္ࣼ൞ඪ,ॖၛ০Ⴈഈඍ4ᇕఅၳ௹ಃބؓႋ์ၛࠣః٤ѓሙ่ॻ.གྷᅏಊ֥ቆކ∃ປಆگᇅ%CCDB.ሸഈॖᆩ,ॖඁ ࠎЧژݼ߭ॖሇߐ์གྷᅏಊંࡎᆴॖၛіղູॉ੮၂ٺഈඍॖඁ߭ॖሇߐ์གྷᅏಊ.ၛ CCDB(S0,T)=(BF/P1)ABCi(S0,T;P2 P1)+BFaP1ބTٳљіൕః૫ᆴaሇߐࡎ۬ބഺჅ௹iཋ(BF/P1)UOC(S0,T;P1)+ABC(S0,T;BF)-;ၛP2іൕડቀඁ߭ೈჿඏ่ࡱൈѓ֥ܢࡎ෮сྶղ֥֞ඁ߭Ԩؿࡎ,۬ཁಖႵP2>P1.ೂՎABCd(S0,T;BF)+DB(S0,T)(1),ఃሇߐбੱ(ࡼ၂ٺॖඁ߭ॖሇߐ์གྷᅏಊሇߐཁಖ,ھіղൔౢ༉ֹᅚൕਔCCDB֥ࡎᆴቆӮ.Ӯ௴๙ܢௐ෮ିࠆ֤֥௴๙ܢௐ֥ඔਈऌᆭ,҂ࣇॖၛປಆگᇅCCDB,طॖၛႵᆌؓ)ॖၛіൕູྟֹؓԊ۲ቆӮ҆ٳ֥หႵڄག.(BF/P1).ൈ,ၛCCDB(S0,T)іൕھሇᅏ֥֒భંࡎᆴ,ၛDB(S0,T)іൕაᆭؓႋ֥์གྷᅏಊ(discountbond,ႵሢဢЧࣁބഺჅ3 ં ᆣ௹ཋ)֥֒భંࡎᆴ.Վຓ,ູіղࡥࢱ,ࡼ֒భൈख़ቔູਬൈख़,ѩၛS0aS ބSTٳљіൕᄝଁี ॖඁ߭ॖሇߐ์གྷᅏಊॖၛФປಆ֒భൈख़a ൈख़ބ֞௹ൈख़֥ѓ֥ܢࡎ,ఃᇏҷࢳູၛ༯5ᇕࡥֆᆣಊ֥ቆކ:ਆᇕܥקᆦڱ0< <Tح҂֥৫ࠧᆦڱܿᄵૅൔؽᆴઙಃa၂ᇕܿ. ປಆҷࢳᄵഈీԛઙಃa၂ᇕӾᆦڱܿᄵૅൔؽᆴઙ൙ൌഈ,ॖၛࡼCCDBुቔؓႋ์གྷᅏಊڸಃބ၂ᇕؓႋ์གྷᅏಊ,ࠧൔ(1)Ӯ৫.ࡆਔᆳྛൈख़҂ಒקطᆳྛࡎ۬҂ಒק֥൬ၭ ࠎЧࡌഡٿפ֥ਫ਼ࣥ၇ঠఅၳ௹ಃ.ູՎ,҂ᄜၛ௴๙௹ࡌഡ1 ܱႿሧЧ൧ӆ,ҐႨBlack Scholesಃ,ط൞ၛఅၳ௹ಃࣉྛҷࢳ.ቋᇔ,ࡼCCDB∃ປ௹ಃଆࡌഡॿࡏ[22].࣐ܵھࡌഡॿࡏཌྷؓॎಆҷࢳ%ູ༯ඍ5ᇕཌྷؓࡥֆᆣಊ֥ቆކ,ఃҷࢳख़,࣐ܵᄀটᄀ؟໓ངᄝקࡎ௴๙௹ಃൈՖ۲ٚݖӱೂ༯.૫Ӈ൫٢ॺھࡌഡॿࡏ,൞ᄝູگᄖ֥စളᆣֻ1҄,ࡼCCDBປಆҷࢳູਆᇕᆣಊ:ሧಊࣉྛקࡎ,Ⴍఃေࠆ֤ࢳ༅ൔൈ,གྷႵ໓ང၂ϮᆀႚႵ֥aٺඔູ(BF/P1)aᅰθඣູP2aܥקಯಖҐႨھࡌഡॿࡏ.ࡥေটඪ,ھॿࡏᇶေЇওᆦڱحູ(P2-P1)֥৫ࠧᆦڱܿᄵૅൔؽᆴ4۱ٚ૫: ሧЧ൧ӆ൞ଉ҈൧ӆ;!թᄝ৵࿃ઙಃABCi(S0,T;P2-P1)(Americanbinaryڄག০ੱr,طః௹ཋࢲܒ౷ཌ൞ඣ;֥∀calls)ބ၂ᇕ٤ܿᄵఅၳ௹ಃ.ֻ2,҄Ֆ෮֤٤҂թᄝڄགส০ࠏ߶;&ܢࡎڛՖೂ༯ঔܿᄵఅၳ௹ಃᇏҷࢳԛ:ሧᆀႚႵ֥aٺඔູݖӱ(BF/P1)aᆳྛࡎູ۬P1aᅰθඣູP2֥ܿᄵdS= Sd + SdWP(2)ഈీԛઙಃUOC(S0,T;P1)(up and outcalls).ఃᇏ,WP൞၂۱קၬᄝປСۀੱॢࡗ(!,F,P)ֻ3,҄ࡼഺჅ҆ٳ֥٤ܿᄵఅၳ௹ಃປಆҷࢳᇏ֥ڛՖѓሙົବݖӱ֥ෛࠏэਈ; ބ ٳљ
138 ܵ ॓ ࿐ ࿐ Б2009୍8ᄅіൕѓ֥ܢࡎ֥௹ຬ൬ၭੱބѯ.ੱ၂Ϯֹ, ඁ߭ಃൈ,ሧᆀࡼႚႵೂ༯ਆᇕ࿊ᄴ:ࠇᆀࢤ൳Фࡌקູܥקӈඔ.ؿྛᆀ֥ඁ߭གྷࣁ(ఃնཬູሇᅏඁ߭ࡎ۬),ࠇЧ໓ҐႨBlack Scholes௹ಃଆࡌഡॿࡏ,ᆀ৫ࠧᆳྛሇߐಃ,ࠆ౼֒ൈ֥ሇߐࡎᆴ.ᄝൌ࠽ၩሢ෮ࡹקࡎଆູࠎႿܢࡎ֥ֆၹሰส০ሇᅏ൧ӆᇏ,Ⴍఃᄝᇏݓሇᅏ൧ӆᇏ,ؿྛᆀ༐ଆ.Ⴎ໓ང[4]ބ[6]ॖᆩ,ᄝູॖሇߐᅏಊקຬሧᆀ࿊ᄴᆳྛሇߐಃ,ၹՎᄝഡ࠹ሇᅏ่ॻࡎൈ,ೂݔ০ੱᄝކٓຶଽ౼ᆴ,ପહֆၹሰൈ,ඁ߭གྷࣁح၂ϮФഡקູཬႿડቀඁ߭ೈჿส০ଆაਆၹሰส০ଆཌྷб,ਆᆀקࡎࢲඏ่ࡱൈ֥ሇߐࡎᆴ,Ֆطؿྛᆀॖၛ๙ݖ࿆ۡݔҵၳޓཬ.ၹՎ,ࡌഡڄག০ੱ௹ཋࢲܒ౷ཌඁ߭ট௧ሧᆀ࿊ᄴᆳྛሇߐಃ.২ೂ,֒ܢௐ൞ඣ֥,൞ࠎЧކ֥.ࡎ۬ղ֞ࠇӑݖሇߐࡎ֥۬130%ൈ,ؿྛᆀႵࡌഡ2 ॖሇߐᅏಊؿྛᆀ(ؿྛ܄ඳܵಃοᅶሇᅏ૫ᆴ֥105%ᆳྛඁ߭ಃ.ࡌקఃሇҪ)ބሧᆀ(ЇওӻႵᆀၛࠣյෘӻႵ֥ሧߐࡎູ۬10ჭ,ః૫ᆴູ100ჭ.֒ѓ֥ܢࡎղ֞ᆀ)൞ປಆྟ,֥طሹ൞ொݺ۷؟ҍڶ.ؓ13ჭൈ,ࡼડቀඁ߭ೈჿඏ่ࡱ,ᄝંഈؿྛႿӻႵᆀ,ሹ൞࿙ॖሇߐᅏಊࡎᆴ֥ቋն߄.ؓᆀႋھ৫࿆ࠧۡᆳྛඁ߭ಃ.Վൈඁ߭གྷࣁحᆺႿؿྛᆀ,ቔູܢתಃၭ֥սದ,ሹ൞࿙ܢתႵ105ჭ,ط৫ࠧᆳྛሇߐಃ෮֤ሇߐࡎᆴູҍڶ֥ቋն߄,ࠧܢࡎቋն߄.McConnellބ100∋10#13=130ჭ.ཁಖ,ᄝᆃᇕ౦ঃ༯,ӻႵ][14]Schw[10artzၛࠣBarone Adesi֩ᇭ؟໓ངᆀࡼФ௧࿊ᄴᆳྛሇߐಃ.ᆞၹೂՎ,ջႵඁ߭ೈࣉྛਔဢࡌഡ.ჿඏ่ࡱ֥ඁ่߭ॻႻФӫູ∃఼ᇅሇߐ่ॻ%.ࡌഡ3 ؿྛᆀބሧᆀ(ЇওӻႵᆀၛࠣ ڄགᇏྟൗࢸյෘӻႵ֥ሧᆀ)ऎႵؓӫ൧ӆྟႮ໓ང[24]ॖᆩ,ᄝഈඍࠎЧࡌഡ༯,(symmetricmarketrationality).္ࣼ൞ඪ,ૌିܔྟყ௹֞дՎ֥ቋႪथҦ.২ೂ,ؓႿॖඁ߭dWP=dWP -r-d ,ఃᇏ,WP൞၂۱קၬᄝປ ॖሇߐᅏಊط,ؿྛᆀିܔყ௹֞ӻႵᆀࡼҐСۀੱॢࡗ(!,F,P)༯֥ڛՖѓሙົବݖӱ֥౼֥ቋႪሇߐҦ,ൈሧᆀ(ЇওӻႵᆀၛෛࠏэਈ.ಖު,ࡼᆭսೆൔ(2),ॖ֤ᄝڄགᇏࠣյෘӻႵ֥ሧᆀ)္ିܔყ௹֞ؿྛᆀࡼҐྟൗࢸѓ֥ܢࡎࡼڛՖೂ༯ঔݖӱ౼֥ቋႪඁ߭Ҧ[1].Ingersoll္ࣉྛਔဢࡌഡ.dS=rSd + SdWP(3)ࡌഡ4 మᄝ∃༎ིႋ(dilutioneffect)%ॖ,ჰট֥ ၘФ৵࿃ڄག০ੱr౼ս,҂ݖ,ၘّࣜ႘ᄝ֒భѓ֥ܢࡎᆭᇏ.္ࣼ൞ඪ,ᄝӻႵჰট֥ѯੱ ѩໃ൳֞ۀੱҩ؇ሇߐ֥႕ཙ.ᆀࡼॖሇߐᅏಊሇߐູ௴๙ܢௐൈ,ѩ҂߶֝ᇁႮႿൔ(3)ᇏᄜఃҕඔაڄགொݺႵ,ܱၹѓ֥ܢࡎ֥ᇧಖ༯ࢆ.ႮႿሧᆀ൞ປಆྟՎ,ᄝೂՎۀੱҩ؇ሇߐᆭު,ॖሇߐᅏಊקࡎ໙,֥ିܔྟყ௹֞ॖሇߐᅏಊᄝࡼটФሇߐູีࣼॖၛՖႵሢڄགொݺ֥གྷൌൗࢸሇ၍֞ڄག௴๙ܢௐ֥ॖିྟնཬ,ၹՎೂՎࡌഡ൞ࠎЧކᇏྟൗࢸ.္ᆞೂՎ,PФӫᆭູڄགᇏྟۀੱҩ֥[23],ೂConnolly෮ඍ.؇.Ⴎڄགᇏྟקࡎંॖᆩ,ᄝڄགᇏྟൗࢸ, ቋႪሇߐҦބቋႪඁ߭Ҧ෮ႵሧӁ֥௹ຬ൬ၭੱ൞৵࿃ڄག০;ੱطᄝഈඍࡌഡࠎԤഈ,Ⴎ໓ང[10]ॖᆩ:(1),ଖ၂ᆣಊ֥௹Ԛࡎᆴ൞௹ᇔࡎᆴ֥གྷᆴ,ఃሧᆀቋႪሇߐҦູ:ᄝ֞௹భ,҂ႋھᇶᆳ์གྷੱູ৵࿃ڄག০.ੱྛሇߐಃ,Ԣ٤ؿྛᆀ࿆ۡᆳྛඁ߭ಃ;ᄝ֞௹ ܢࡎਫ਼݂ࣥোൈ,ሇߐࡎᆴնႿCCDB֥૫ᆴ,ᄵᇶᆳྛሇᄝഈඍڄགᇏྟൗࢸ,ॖၛࡼໃটॖିؿളߐಃ,ڎᄵሧᆀႋھေؿྛᆀၛགྷࣁඁ֥߭ѓ֥ܢࡎਫ਼ູ݂ࣥ༯ඍ3ো,ೂ1෮ൕ.CCDB,ఃඔحູCCDB֥૫ᆴ.(2)ؿྛᆀቋႪਫ਼ࣥ1 ᄝഺჅ௹ཋଽ,ѓ֥ܢࡎ၂؇ഈᅨඁ߭Ҧ൞ᄝഺჅ௹ཋଽ,ᆺေѓ֥ܢࡎഈᅨ֞֞ඁ߭Ԩؿࡎ.۬҂ٞၛ *іൕՖ֒భൈख़֞ѓඁ߭Ԩؿࡎ۬,ؿྛᆀႋھࠧख़࿆ۡᆳྛඁ߭ಃ.֥ܢࡎ൮Ցഈᅨ֞ඁ߭Ԩؿࡎ۬ൈ֥ൈࡗ؍ӉႮႿ҂թᄝඁ߭๙ᆩ௹,֒ؿྛᆀ࿆ۡᆳྛ؇,ପહھোܢࡎਫ਼ࣥॖၛіൕູ *(T.
ֻ4௹ᇛఃჷ֩:ॖඁ߭ॖሇߐ์གྷᅏಊປಆҷࢳקࡎم 139 ਫ਼ࣥ2 ѓ֥ܢࡎ၂ᆰໃିഈᅨ֞ඁ߭ԨؿၹՎॖၛࡼ(BF/P1)ֆ໊֥ABCi(S0,T;P2-P1)ࡎ۬,൞֞௹ൈھሇᅏ֥ሇߐࡎᆴնႿః૫ᆴ,ބABCi(S0,T;BF)ކѩູၛP2ູᅰθඣaၛࠧѓ֥ܢࡎնႿሇߐࡎ,۬ପહھোܢࡎਫ਼ࣥॖ(BF/P1)P2ູܥקᆦڱح֥৫ࠧᆦڱܿᄵૅၛіൕູ *>TST>P1.ൔؽᆴઙಃABCi(S0,T;(BF/P1)P2).ູਔაၛਫ਼ࣥ3 ѓ֥ܢࡎ၂ᆰໃିഈᅨ֞ඁ߭Ԩؿສҷࢳٚمࣉྛབྷ༥бࢠ,Ч໓ᄠໃކѩ.ࡎ۬,ط֞௹ൈѓ֥ܢࡎ҂նႿሇߐࡎ۬,ࠧ ᆣૼ* >TST(P1.ᆣૼ ᄝڄགᇏྟൗࢸ,၇ऌሧᆀቋႪሇູіඍٚь,ഡקਆ۱൙ࡱ:A൙ࡱ ᄝߐҦބؿྛᆀቋႪඁ߭Ҧॖᆩ:֒Paths1ؿഺჅ௹ཋଽ,ѓ֥ܢࡎ၂؇ഈᅨ֞ඁ߭Ԩؿࡎ۬;ളൈ,ؿྛᆀࡼᄝѓ֥ܢࡎ൮Ցղ֞ඁ߭ԨؿࡎB൙ࡱ ֞௹ൈѓ֥ܢࡎնႿሇߐࡎ.۬ೂ֥۬ൈީ,৫࿆ࠧۡᆳྛඁ߭ಃ,ՎൈሧᆀࡼФՎ,ॖၛഡק၂۱აਫ਼ࣥ1ཌྷؓႋ֥ൕྟݦඔ௧࿊ᄴᆳྛሇߐಃ,Վൈሇᅏགྷᆴູ-r *(indicatorfunction)IA:A൙ࡱؿള,ఃᆴູ1,e(BF/P1)P2;֒ਫ਼ࣥ2ؿളൈ,ሧᆀࡼᄝ֞҂ؿള,ఃᆴູ0.োර,ֹაਫ਼ࣥ2ބਫ਼ࣥ3ؓ௹ൈᇶᆳྛሇߐಃ,Վൈሇᅏགྷᆴູႋ֥ൕྟݦඔॖၛٳљഡקູ-rTIABބ(BF/P1)ST;֒ਫ਼ࣥ3ؿളൈ,ሧᆀࡼᄝ֞௹ൈေؿྛᆀၛඔحູሇᅏ૫ᆴ֥གྷࣁඁ߭CCDB,Վൈሇᅏགྷᆴູ-rTeBF.ሸഈ,ᄝڄགᇏྟൗࢸ,ॖඁ߭ॖሇߐ์གྷᅏಊ֥ંࡎᆴॖၛіൕູCCDB(S0,T)=-r *e(BF/P1)P2 *(T-rT e(BF/P1)ST *>T,ST>P1-rTeBF *>T,ST(P1=(BF/P1)P2EP-r *[eIA]+(BF/P-rT1)eEP[STIAB]+B-rTFeEP[IAB](8)1 ໃটॖିؿള֥ѓ֥ܢࡎਫ਼݂ࣥোൕၩࡼൔ(4) (7)սೆ,ॖ֤ ཌྷܱఅၳ௹ಃંࡎᆴCCDB(S0,T)={(BF/P1)(P2-P1)+BF}#၇ऌڄགᇏྟקࡎჰ,Ⴎ৫ࠧᆦڱܿᄵ EP-r *rT[eIA]+(BF/P-1)e#ૅൔؽᆴઙಃaܿᄵഈీԛઙಃބӾᆦڱܿP-rTP E{[(ST-P1)+P1]IAB}+BFeE[IAB]ᄵૅൔؽᆴઙಃ֥۲ሱ൬ၭหྟॖ֤,ഈඍr *4ᇕ =(BF/P1)(P2-P1)EP-[eIA]+అၳ௹ಃંࡎᆴॖၛٳљіղູ BFEP-r *rT[eIA]+(BF/P-1)e#ABCi(S0,T;P2-P1)=(P2-P1)# EP[(ST-P1)IAB]+B-rTFeEP[IAB]+EP-r *[eIA](4)T B-rFeEP[IAB]ABCi(S0,T;BF)=B-r *FEP[eIA](5)=(BF/P1)ABCi(S1,T;P2-P1)+UOC(S0,T;P-rT1)=eEP[(ST-P1)IAB] ABCi(S0,T;B-rTEPF)-BFe[IA]+-rT(6) (BF/P1)UOC(S0,T;P1)+BFe#ABCd(S0,T;BF)=B-rTFeEP[IA](7) EP[IA+IAB+IAB]ఃᇏP,E[x]іൕᄝڄགᇏྟۀੱҩ؇P༯ؓэ=(BF/P1)ABCi(S0,T;P2-P1)+ਈxඔ࿐௹ຬ. (BF/P1)UOC(S0,T;P1)+൙ൌഈ,ႮႿiABC(S0,T;P2-P1)ބ ABCi(S0,T;BF)-ABCd(S0,T;BF)+ABCi(S0,T;BF)൞ၛP2ູᅰθඣ֥৫ࠧᆦ DB(S0,T)(9)ڱૅൔؽᆴઙಃ,ື၂҂֥ᆺႵܥקᆦڱح, ܣଁีӮ৫.ᆃ၂ᆣૼݖӱෙಖ൞ᄝڄ
140 ܵ ॓ ࿐ ࿐ Б2009୍8ᄅགᇏྟൗࢸࣉྛ֥,ಖطႮڄགᇏྟקࡎჰॖS0 2ᆩln,ဢൡႨႿགྷൌൗࢸ.P+r+T12d1= T 24 קࡎࢳ༅ൔr+2u^=࣐ܵഈඍ4ᇕఅၳ௹ಃ൞అၳ֥,൞္ 2൞ཌྷؓܿᄵ.֥၇ऌ໓ངࡼൔ(10) (14)սೆൔ(1),ࣼॖၛࠆ֤ॖ[25]ބ[26]ॖᆩ,ഈඍ4ᇕఅၳ௹ಃބ์གྷᅏಊ֥ࡎᆴࢳ༅ൔॖၛіൕູඁ߭ॖሇߐ์གྷᅏಊ֥קࡎࢳ༅ൔ.࣐ܵ෮֤קࡎࢳ༅ൔुഈಀٳگᄖ,ಖطՖҕඔܙ࠹ٚ૫~ABCi(S0,T;P2-P1)=(P2-P1)exp[y(u-u)]#টु,ᆺླܙ࠹ ,ᆃაקࡎ௴๙ܢௐ௹ಃ൞၂ဢ~.֥Վຓ, [N(-a2)+֝ھࢳ༅ൔ෮ླ֥൧ӆࡌഡ่ࡱ,აexp(2yu)N(-a1)](10)UOC(SBlack Scholes௹ಃקࡎଆ္൞၂ဢ֥.ၹՎ,ھ0,T;P1)=c(S0,T)-S0N(x)+ࢳ༅ൔႵሢࢠݺൡႨྟ. P-rT1eN(x- 2u^T)+S0(P2/S0)#2u^-2ൈ,෮֤קࡎࢳ༅ൔ҂ࣇॖၛູCCDBࣉ [N(-z)-N(-z1)]-P-rT1e(P2/S0)#ྛܙᆴ,طॖၛᆰࢤႨট࠹ෘ۲ᇕхགҕඔ,ೂ [N(-z+ T)-N(-z1+ T)](11)DeltaGammaބVega֩,ՖطॖၛႵᆌؓྟֹؓABCd(S0,T;BF)=B-rTFe#Ԋڄག,ߎॖၛᆰࢤႨট࠹ෘCCDBࡎᆴؓႿᇶ [N(-a4)+(P(2r- 2)/ 22/S)N(-a3)](12)ေҕඔ֥ૹۋ༢ඔ,ೂሇߐࡎ۬ބඁ߭Ԩؿࡎ۬~ABCi(S0,T;BF)=BFexp[y(u-u),֩Ֆطॖၛᆌؓؿྛ܄ඳหק౦ঃႪ߄ሇᅏ่]#~ॻ.Վຓ,ߎॖၛࢶᆭࣉྛڄགส০֩.֩ [N(-a2)+exp(2yu)N(-a1)](13)DBrT(S0,T)=B-Fe(14)ఃᇏ5 ඔᆴဒᆣ:~~y+uTy-uTa1=,a2=֒భ,࣐ܵMonteCarloଆקࡎم࠹ෘིੱTT҂ۚ,൞ၘࣜӮູູܼࢤ൳֥စളᆣಊקࡎٚ 2~r-مᆭ၂.ၹՎ,ၛࠎႿଆم֥קࡎࢲݔቔູޙਈ22u=u+2r,u= ഈඍࢳ༅ൔקࡎིݔ֥ѓሙ.ᄝႋႨଆקࡎمPൈ,၇ऌᇏݓሧЧ൧ӆൌ࠽౦ঃ,ၛ1୍Ⴕ240۱2lnS൬ࡎࣉྛଆ,ଆՑඔູ10000Ց,ѩҐႨؓ0y= эਈم(antitheticvariabletechnique)ࡨཬ༂Sҵ.Վຓ,ႮႿഈඍࢳ༅ൔ൞ᄝ৵࿃ॿࡏ༯ࠆ֤0lnP2,֥طଆקࡎم൞ᄝॿࡏ༯ࣉྛ,֥ၹՎభx=+u^ T Tᆀཌྷؓުᆀ,թᄝ৵࿃ொҵ(continuityerrors).ູPਔஆԢ֥႕ཙ,Ч໓ҐႨBroadie֩[27]෮ิԛ2lnS0֥טᆜٚم.ऎุটࢃ,ᄝႋႨഈඍקࡎࢳ༅ൔz=+u^ T Tൈ,ࡼቔູᅰθඣ֥ඁ߭Ԩؿࡎ۬P2טᆜູ2p2P∀ #t2e,ఃᇏ∀)0 =+u^ T၇ऌᇏݓሇᅏ൧ӆൌ࠽౦ঃ,ഡק၂۱ॖඁ T߭ॖሇߐ์གྷᅏಊඔᆴ২ሰ:ູBF=100ჭ,y+uTy-uTaP1=10ჭ,P2=,P1=13ჭ,r=, =3=,a4=TT0 3.ູਔ۷ऎඪڛ৯,ࡼ֒భѓ֥ܢࡎ౼ᆴٓຶTc(S0,T)=S0N(d1)-P-r1eN(d1- T)౼ູS0∗[3,13],ၛູ҄Ӊ,ࡼഺჅ௹ཋ
ֻ4௹ᇛఃჷ֩:ॖඁ߭ॖሇߐ์གྷᅏಊປಆҷࢳקࡎم 141 ٳљ࿊קູ5୍a2୍ބ1୍. C(S0,T;P1)-(BF/P1)C(S0,T;Sc)(15)ᄝഈඍ҂֒భѓ֥ܢࡎބഺჅ௹ཋ༯,ࡼбࢠൔ(1)აൔ(15)ॖ,֤ਟၬཌྷ֩[20]෮ࠎႿࢳ༅ൔ(ࣜݖטᆜ)֥קࡎࢲݔ(ၛ∃analyticิԛ֥ഈඍ࣍රҷࢳ֥ંሹொҵູsolutionwithcorrection%іൕ)აࠎႿଆم֥ErrorLin(S0,T)=CCDB(S0,T)-קࡎࢲݔ(ၛ∃simulationsolution%іൕ)ࣉྛб CCDB(S0,T)Lin(16)ࢠ,ೂ2෮ൕ.бࢠॖᆩ,ંᄝޅᇕሑ༯,ਆູਔࣉྛؓб,࿃ٳ༅ਸ਼၂ᇕ۷ࡥֆ֥ҷᆀҵၳޓཬ,ఃनཌྷؓ༂ҵᆺႵ%,ఃࢳم֥קࡎொҵ.ھҷࢳمؓඁ߭ಃ҂Ⴭॉ੮,ࡥቋնཌྷؓ༂ҵ္ໃӑݖ%.ॉ੮֞Ϝ৵࿃ॿֆֹࡼ၂ٺCCDB࣍රҷࢳູ၂ٺაᆭؓႋ֥௴ࡏטᆜູॿࡏൈႵሢັཬ༂ҵ,Ⴛॉ੮֞ଆ๙Ղᅏಊބ(BF/P1)ٺӻႵᆀႚႵ֥aၛሇߐࡎקࡎمЧദႵሢັཬ༂ҵ,ೂՎҵၳປಆ൞ᆞູ۬ᆳྛࡎ֥۬ൔઙಃ(აሇߐಃཌྷؓႋ),҂ӈ֥.ᆃࣼԉٳဒᆣਔЧ໓֝ݖӱ֥ᆞಒ.ྟ္ٞࡼᆭࡥӫູ∃၂ಃҷࢳم%.ॖၛࡼھ࣍රҷࢳԉٳіૼ,෮ิԛ֥ҷࢳಒൌ൞ປಆҷࢳіղູCCDB(S0,T)sim)DB(S0,T)+ (BF/P1)C(S0,T;P1)(17)бࢠൔ(1)აൔ(17)ॖ,֤ೂՎҷࢳ֥ંொҵູErrorsim(S0,T)=CCDB(S0,T)- CCDB(S0,T)sim(18) 数值例子ಯಖҐႨഈඍCCDBඔᆴ২ሰ,ٳљᇅਔErrorLinބErrorsimაਆሑэਈᆭࡗ֥3ົэܱ༢,ٳљೂ3ބ4෮ൕ,ఃᇏ֒భѓ֥ܢࡎ౼ᆴٓຶഡקູS0∗[3,13],ၛູ҄Ӊ;2 ࠎႿࢳ༅ൔקࡎࢲݔაࠎႿଆקࡎࢲݔᆭࡗ֥бࢠഺჅ௹ཋ౼ᆴٓຶഡקູT∗[0,5],ၛູ҄Ӊ.ཌྷؓЧ໓෮ิԛ֥ປಆҷࢳم,Ⴎ3ॖᆩ,andthosefromsimulationਟၬཌྷ֩[7]෮ิԛ֥ਆಃҷࢳمሹ൞קࡎொ֮,ط,֒భѓ֥ܢࡎჟۚ,ഺჅ௹ཋჟӉ,ఃொ֮6 ႋ Ⴈږ؇ჟն;Ⴎ4ॖᆩ,ഈඍ၂ಃҷࢳمሹ൞קࡎொۚ(Zᇠቕѓູڵ),ط,֒భѓ֥ܢࡎჟۚ, ၛສҷࢳٚم֥קࡎொҵഺჅ௹ཋჟӉ,ఃொۚږ؇ჟն.ᆴ֤ᇿၩ֥൞, 理论偏差ᄝؓႋሑ༯,ᆰࢤбࢠErrorLinބErrorsim֥ध࠻ಖЧ໓෮ิԛ֥ҷࢳ൞ປಆҷࢳ,ପહაؓᆴॖᆩ,ErrorLinሹ൞նႿErrorsim.ඪૼ,ࠎႿഈᆭбࢠ,ॖ֤ၛສҷࢳم֥קࡎொҵ.༵টٳ༅ਟඍਆಃҷࢳم֥קࡎொҵൌ࠽ഈߎնႿࠎႿഈඍၬཌྷ֩[20]෮ิԛ֥ҷࢳ.ࡥֆটࢃ,ૌࡼ၂ٺ၂ಃҷࢳم֥קࡎொҵ.CCDB࣍රҷࢳູ:၂ٺაᆭؓႋ֥௴๙Ղᅏಊ CCDBંࡎᆴაਆሑэਈᆭࡗܱ༢DB(S0,T),(BF/P1)ٺӻႵᆀႚႵ֥aၛሇߐࡎCCDBંࡎᆴႵሢਆ۱ሑэਈ:֒భѓູ۬ᆳྛࡎ֥۬ૅൔઙಃ(აሇߐಃཌྷ֥ؓܢࡎބഺჅ௹ཋ.ູՎ,ಯಖҐႨഈඍCCDBඔႋ)C(S0,T;P1),ބ(BF/P1)ٺؿྛᆀႚႵ֥aᆴ২ሰ,ᇅ3ົ৫ุটॉҳCCDBંࡎᆴၛඁ߭ࡎູ۬ᆳྛࡎ֥۬ૅൔઙಃ(აඁ߭ಃཌྷაਆሑэਈᆭࡗ֥3ົэܱ༢,ೂ5෮ൕ,ؓႋ)C(S0,T;Sc),҂ٞࡼᆭࡥӫູ∃ਆಃҷࢳఃᇏ֒భѓ֥ܢࡎ౼ᆴٓຶഡקູS0∗[3,13],م%.ॖၛࡼھ࣍රҷࢳіղູၛູ҄Ӊ;ഺჅ௹ཋ౼ᆴٓຶഡקູT∗[0,CCDB(S0,T)Lin)B(S0,T)+(BF/P1)#5],ၛູ҄Ӊ.
142 ܵ ॓ ࿐ ࿐ Б2009୍8ᄅ Ⴎ5ॖᆩ,CCDBંࡎᆴሹ൞֒భѓ֥ܢࡎ֥ᄹݦඔ,ࠧхགҕඔDeltaሹ൞ູᆞ,طఃܱ༢౷ཌ֥౷؇,ෛሢഺჅ௹ཋ֥ࡨཬطᇯࡶᄹն.ᆴ֤ᇿၩ֥൞,CCDBંࡎᆴѩ٤ሹ൞ഺჅ௹ཋ֥ᄹݦඔ,ᄝധ؇ྴᆴሑ༯,ّط൞ഺჅ௹ཋ֥ࡨݦඔ.൙ൌഈ,൞ഺჅ௹ཋ֥ᄹݦඔ,ߎ൞ࡨݦඔ,౼थႿఃଽݣ௹ಃࡎᆴᄹӉ؇ބ์གྷᅏಊࡎᆴࡨཬ؇ᆭࡗ֥ܱ༢.ᄝധ؇ྴᆴሑ༯,ෛሢഺჅ௹ཋ֥ᄹӉ,ଽݣ௹ಃࡎᆴᄹӉ؇ཬႿ์གྷᅏಊࡎᆴࡨཬ؇,CCDBંࡎᆴࣼ൞ഺჅ௹ཋ֥ࡨݦඔ,ಖط,ෛሢ֒భѓ֥ܢࡎࡶࡶэն,ଽݣ௹ಃࡎᆴᄹӉ؇ࡶࡶิۚ,ط์གྷᅏಊࡎᆴࡨཬ؇ѩໃэ߄,ၹՎ,၂֊֒భѓ֥ܢࡎᄹն֞၂קӱ؇ൈ,ଽݣ௹ಃࡎᆴᄹӉ؇ࡼնႿ์གྷᅏಊࡎᆴࡨཬ؇,ՎൈCCDBંࡎᆴࡼэູഺჅ௹ཋ֥ᄹݦඔ.္ࣼ൞ඪ,၂Ϯ,ֹෛሢ֒భѓ֥ܢࡎ֥Ֆཬ֞ն,хགҕඔThetaᇯࡶࡨཬ,طႵሢ၂۱Ֆᆞᆴэູڵᆴ֥ݖӱ.7 ࢲඏეᄝBlack Scholes௹ಃଆࡌഡॿࡏ༯,Ч໓ᆌؓၛສҷࢳٚم֥҂ቀ,ሇэනਫ਼,҂ᄜ০Ⴈ௴๙௹ಃ,ط൞০Ⴈఅၳ௹ಃ,ࡼॖඁ߭ॖሇߐ์གྷᅏಊ∃ປಆҷࢳ%ູؓႋ์གྷᅏಊބ3ᇕཌྷؓࡥֆ֥అၳ௹ಃ,ѩࢶᆭࠆ֤ఃקࡎࢳ༅ൔ.ႮႿ෮ླ൧ӆࡌഡ่ࡱބҕඔܙ࠹აBlack Scholes௹ಃקࡎ܄ൔ൞၂ဢ֥,ھࢳ༅ൔႵሢࢠݺ֥ൡႨ.ྟՎຓ,ھࢳ༅ൔ,ߎॖၛႨট࠹ෘ۲хགҕඔၛࠣࣉྛڄགส০,֩.֩ൈ,Ч໓௩༅ਔၛສҷࢳקࡎم֥ொҵ,ѩᅚൕਔॖඁ߭ॖሇߐ์གྷᅏಊંࡎᆴაਆሑэਈᆭࡗ֥3ົэܱ༢.ᆃсࡼննႵᇹႿݓሇᅏሧᆀӞࢳሇᅏࡎᆴቆӮ,ѩކܙ࠹ሇᅏࡎᆴ.҂ቀ֥൞,ؓႿթᄝᅏ༏a෭ק௹ބྐႨڄག֩౦ঃ,൞ڎ၇ಖॖၛປಆҷࢳ,ഉླࣉ၂࣮҄.ҕॉ໓ང:[1][J].JournalofFinancialEconomics,1977,4:289 322.[2]BrennanMJ,:Valuationandoptimalstrategiesforcallandconversion[J].JournalofFi
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144 ܵ ॓ ࿐ ࿐ Б2009୍8ᄅAnalyticvaluationofthecallableconvertiblediscountbonds:EquivalentdecompositionmethodZHOUQ1,2i yuan,WUC1hong feng,LIUH1ai &Managemen,tShanghaiJiaotongUniversity,Shanghai200052,China;.,Shanghai200120,ChinaAbstract:UndertheBlack Scholesframework,accordingtotherisk neutralvaluationprincipa,lwepresentanequivalentdecompositionmethodfortheCallableConvertibleDiscountBonds(CCDB).Basedonthismethod,weequivalentlydecomposeoneCCDBintotheportfoliooffivekindsofsimpleandtradablesecuri ties:tworegularAmericanBinaryCallswithimmediately madefixedpayments,oneregularUp and OutCal,loneregularAmericanbinarycallwithafixedpaymentthatisdeferreduntilmaturity,,,,thismethodcannotonlygivemuchnewinsighttothevaluecompositionofCCDB,:callableconvertiblediscountbonds;equivalentdecompositionmethod;up and outcal;lAmeri canbinarycalls;derivativepricing(ഈࢤֻ114်) mandinformationispooledatthesupplier,thesupplierandtheretailerswillobtaindifferentinformation,(PIE).ToanalyzeconditionsforPIE,,wepresentthesufficientconditionforPIEinmulti ,wepresentthesufficientconditionforPIEinmulti periodsupplychainswhenthemyopicinventorystrategyisadoptedandthatinathree periodsupplychainwhenopti ,weanalyzetherelationshipamongthebullwhipeffec,tin :supplychainmanagemen;tunknowndemand;pooledinformationeffec;tinformationsharing
