Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ࣁವ۽ӱֻඹᅣ௹ಃࡎ֥۬ૹۋྟބ௹ಃ֥ส௹Ќᆴ༰ն࿐ࣁವ༢Copyright©2009Zheng,Zhenlong&Chen,Rong2009୍05ᄅ19ರࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ଢDeltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ଢDeltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Delta֥קၬ௹ಃ֥Deltač∆Ďᆣಊ֥Deltač∆Ď൞ᆣಊࡎ۬ؓѓ֥ሧӁࡎ֥۬၂ࢨொ֝ඔ∆=∂f∂Sࠫޅഈটुđ௹ಃ∆൞௹ಃࡎ۬აѓ֥ሧӁࡎܱ۬༢౷ཌ్֥ཌོ֥ੱb௹ಃ∆іൕᄝః่ࡱ҂э֥౦ঃ༯đѓ֥ሧӁࡎ֥۬ັཬэ෮֝ᇁ֥௹ಃࡎ֥۬эđޙਈਔᆣಊࡎ۬ؓѓ֥ሧӁࡎ۬э֥ૹۋ؇bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Delta֥קၬ௹ಃ∆֥࠹ෘ൬ၭሧӁൔुᅨ௹ಃ֥∆ᆴູ∆=N(d1)൬ၭሧӁൔुי௹ಃ֥∆ᆴູ∆=−N(−d1)=N(d1)−1ᆦڱၘᆩޣ০ੱq֥ൔुᅨ௹ಃ֥∆ᆴູ∆=−q(T−t)eN(d1)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆֥ྟᇉۀੱٳ֥҃ྟᇉğ06N(d1)61൬ၭሧӁुᅨ௹ಃ֥∆ᆴᄝ0ބ1ᆭࡗđ൬ၭሧӁुי௹ಃ֥∆ᆴᄝ−1ބ0ᆭࡗ൬ၭሧӁुᅨ௹ಃॢ֥∆ᆴᄝ−1ބ0ᆭࡗđ൬ၭሧӁुי௹ಃॢ֥∆ᆴᄝ0ބ1ᆭࡗđࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴބѓ֥ሧӁࡎ۬ᆭࡗ֥ܱ༢Ֆd1֥קၬॖᆩđ௹ಃ֥∆ᆴ౼थႿSaraσބT−tbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴބѓ֥ሧӁࡎ۬ᆭࡗ֥ܱ༢(cont.)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴބ֞௹௹ཋᆭࡗ֥ܱ༢ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴބ֞௹௹ཋᆭࡗ֥ܱ༢(cont.)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴބڄག০ੱᆭࡗ֥ܱ༢၂Ϯطڄག০ੱᄀۚđ൬ၭሧӁुᅨ௹ಃބൔुי௹ಃ֥∆ᆴ္ᄀۚࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴބڄག০ੱᆭࡗ֥ܱ༢(cont.)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴაσᆭࡗ֥ܱ༢ѓ֥ሧӁࡎ۬ѯੱؓ௹ಃ∆ᆴ֥႕ཙࢠಒקđ౼थႿڄག০ੱඣaSაX֥ҵएa௹ಃႵི௹֩ၹbؓႿࢠധ؇ྴᆴ֥ुᅨ௹ಃބࢠധ؇ൌᆴ֥ुי௹ಃটඪđ∆൞σ֥־ᄹݦඔbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴაσᆭࡗ֥ܱ༢(cont.)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃDeltaᆴ֥ྟᇉބหᆘٳ༅௹ಃ∆ᆴაσᆭࡗ֥ܱ༢(cont.)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ᆣಊቆކ֥Deltaᆴఃᆣಊ֥∆ᆴ௹ಃѓ֥གྷࠊሧӁ֥∆ᆴູ1bჹ௹ކჿ֥∆ᆴဢູ1b൬ၭሧӁބᆦڱၘᆩགྷࣁ൬ၭሧӁ֥௹ࠊކჿ֥∆ᆴູ∆=r(T−t)eᆦڱၘᆩ৵࿃൬ၭੱqሧӁ֥௹ࠊކჿ֥∆ᆴູ∆=(r−q)(T−t)eഈඍ∆൞ᆌؓ؟ط֥đॢژݼཌྷّbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ᆣಊቆކ֥Deltaᆴᆣಊቆކ֥∆ᆴᆣಊቆކ֥∆ᆴ֩Ⴟቆކᇏֆ۱ሧӁ∆ᆴ֥ሹބčѓ֥ሧӁཌྷĎ∑n∆=wi∆ii=1ఃᇏđwiіൕֻiᇕᆣಊ֥ඔਈđ∆iіൕֻiᇏᆣಊ֥∆ᆴbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Deltaᇏྟሑაส௹Ќᆴ∆ᇏྟሑ∆ᆴູ0֥ᆣಊቆކФӫູԩႿ∆ᇏྟሑb֒ᆣಊቆކԩႿ∆ᇏྟሑൈđቆކ֥ࡎᆴ҂൳ѓ֥ሧӁࡎ۬ѯ֥႕ཙđՖطൌགྷཌྷؓѓ֥ሧӁࡎ֥۬ส௹ЌᆴbԢਔѓ֥ሧӁЧദބჹ௹ކჿ֥∆ᆴޚ֩Ⴟ1đఃစളӁ֥∆ᆴॖିෛൈ҂؎э߄bၹՎᆣಊቆކԩႿ∆ᇏྟሑᆺିົӻ၂۱ޓ؋֥ൈࡗbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Deltaᇏྟሑაส௹Ќᆴ∆ᇏྟส௹Ќᆴ∆ᇏྟЌᆴ֥ൌགྷğᄎႨ၂ѓ֥ሧӁ֥གྷࠊa௹ಃބ௹ࠊ֩ࣉྛཌྷส௹Ќᆴđᆣಊቆކ֥∆ᆴ֩Ⴟ0b∆ᇏྟЌᆴ֥หׄğส௹Ќᆴđླေ҂؎טᆜЌᆴժၛЌᆴቆކᇗྍԩႿ∆ᇏྟሑđᆃᇕטᆜӫູᄜनޙčRebalancingĎbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Deltaᇏྟሑაส௹Ќᆴσ২ğ௹ಃ֥DeltaᇏྟЌᆴଖࣁವࠏܒᄝOTC൧ӆԛ൲ਔࠎႿ100000ܢ҂ڱޣ০ܢௐ֥ൔुᅨ௹ಃđ൬ೆ$300000bھܢௐ֥൧ӆࡎູ۬49ૅჭđᆳྛࡎູ۬50ૅჭđڄག০ੱູ৵࿃گ০୍০ੱ5%đܢௐࡎ୍۬ѯੱູ20%đए֞௹ൈࡗູ20ᇛbႮႿھࣁವࠏܒمᄝ൧ӆഈᅳ֞ཌྷႋ֥ुᅨ௹ಃ؟ؓԊđᆃဢࣼ૫ਢሢڄག֥ܵ໙ีbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Deltaᇏྟሑაส௹Ќᆴσ২ğ௹ಃ֥DeltaᇏྟЌᆴ(cont.)∆ᇏྟЌᆴمႨѓ֥ሧӁčܢௐĎ؟ູՎ௹ಃࣉྛส௹ЌᆴҠቔbႋࣉྛส௹ЌᆴđၛົӻሧӁቆކ֥∆ᇏྟbᄝൌ࠽ᇏđݖႿَ֥טᆜླေཌྷ֥֒ࢌၞٮႨđၹՎૌࡌഡЌᆴטᆜૄᇛࣉྛ၂ՑbཌྷܱҕඔູS=49,X=50,r=,σ=,T−t=ؓԊଆݖӱҕुіࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Deltaᇏྟሑაส௹Ќᆴࢳ௹ಃ֥DeltaᇏྟЌᆴ௹ಃ∆ᇏྟส௹Ќᆴ֥ࢲݔ൞ğૌ๙ݖѓ֥ሧӁܒӮਔ၂۱oކӮ֥௹ಃժpbส௹Ќᆴ֥ӮЧᇶေটჷႿoઙۚછ֮p֥ݖӱđఃሹӮЧᆞݺ֩Ⴟ൧ӆഈཌྷႋ֥௹ಃࡎ۬bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Deltaᇏྟሑაส௹Ќᆴࢳ௹ಃ֥DeltaᇏྟЌᆴ(cont.)ᄝൌ࠽Ҡቔᇏđ∆ᇏྟЌᆴٚم۷ӈ֥൞০Ⴈᇕѓ֥ሧӁ֥௹ࠊժটࣉྛЌᆴđॖၛࠆ֤ۗۆቔႨbၛ൬ၭሧӁ௹ࠊކჿູ২đႮႿ∆=r(T−t)eđᆃၩሢ−r(T−t)e۱௹ࠊֆ໊ؓѓ֥ሧӁࡎ۬э֥ૹۋྟა၂۱ѓ֥ሧӁؓఃሱദࡎ۬э߄֥ૹۋྟ൞ཌྷ֥đၹՎQF=−r(T−t)eHA/Nࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Deltaᇏྟሑაส௹Ќᆴࢳ௹ಃ֥DeltaᇏྟЌᆴ(cont.)∆ส௹Ќᆴ֥ၩၬğ.1..ህြ֥ࣁವᄎႏބڄགᄎႏࠏܒ֥ࡎ۬Ⴊ൝..ࠏܒଽ֥҆ڄགؓԊၛࠣຓ҆൧ӆഈ֥࣪∆ส௹Ќᆴ..ۚ؇ਲࠃྟğࣁವࠏܒॖၛࢲކሱദ֥ሧӁሑঃa൧ӆყ௹ބڄགଢѓটܵ∆ᆷѓđ҂ଢѓ∆ᆴ֥ഡקॖၛൌགྷ҂֥ڄགܵҦbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ଢDeltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................etaקၬΘᆴ֥קၬᆣಊ֥etačΘĎ൞ᆣಊࡎ۬ؓൈࡗt֥ொ֝ඔΘ=∂f∂t௹ಃΘ൞ᄝః่ࡱ҂э౦ঃ༯௹ಃࡎ۬э߄აൈࡗэ߄֥бੱđႨႿޙਈ௹ಃࡎ۬ؓൈࡗэ߄֥ૹۋ؇đޙਈ௹ಃ֥ࡎᆴෛሢൈࡗ၍طᇯࡶකࡨ֥ӱ؇bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................࠹ෘ௹ಃetaᆴ௹ಃΘᆴ֥࠹ෘᄝBSM௹ಃקࡎॿࡏ༯đؓႿ൬ၭሧӁ֥ൔބૅൔुᅨ௹ಃطΘ=−SN′√(d1)σ2T−−rXe−r(T−t)N(d2)t۴ऌѓሙᆞٳ֥҃หྟđN′(x)=√1−x2e22piࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................࠹ෘ௹ಃetaᆴ௹ಃΘᆴ֥࠹ෘ(cont.)ၹՎؓႿ൬ၭሧӁ֥ൔބૅൔुᅨ௹ಃđΘ=−Sσ−d21√e2−r(T−t)rXe−N(d2)22pi(T−t)ؓႿ൬ၭሧӁ֥ൔुי௹ಃđΘ=−Sσ−d21√e2+rXe−r(T−t)[1−N(d2)]22pi(T−t)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃetaᆴ֥ྟᇉބหᆘΘᆴ֥ྟᇉ௹ಃ֥Θӈӈ൞ڵ֥ğ၂Ϯটඪđෛሢ֞௹ರ֥ਢ࣍đ௹ಃࡎᆴᇯࡶකࡨbؓႿԩႿൌᆴሑ֥൬ၭሧӁൔुי௹ಃބԩႿൌᆴሑ֥ޓۚ০ੱ֥ຓ߸֥ൔुᅨ௹ಃđΘॖିູᆞb௹ಃ֥Θᆴൈ൳SaT−tarބσ֥႕ཙbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃetaᆴ֥ྟᇉބหᆘΘᆴބѓ֥ሧӁࡎ۬ᆭࡗ֥ܱ༢ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃetaᆴ֥ྟᇉބหᆘΘᆴބ֞௹௹ཋᆭࡗ֥ܱ༢ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................etaᆴაส௹ЌᆴΘᆴაส௹ЌᆴႮႿൈࡗ֥၍൞ಒק֥đીႵڄགॖbၹՎླؓൈࡗࣉྛส௹ЌᆴbΘა∆ބΓႵࢠն֥ܱ༢bᄝ௹ಃࢌၞᇏđႭః൞ᄝҵ௹ࢌၞᇏđႮႿΘᆴ֥նཬّ႘ਔ௹ಃܓઙᆀෛൈࡗ၍෮ാ֥ࡎᆴđၹطંؓႿхགᆀaส০ᆀߎ൞ሧᆀطđΘᆴ൞၂۱ᇗေ֥ૹۋྟᆷѓbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ଢDeltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃGamma֥קၬ௹ಃΓקၬ௹ಃ֥Gamma(Γ)൞௹ಃࡎ۬ؓѓ֥ሧӁࡎ֥۬ؽࢨொ֝ඔđࠇ௹ಃ∆ؓѓ֥ሧӁࡎ֥۬၂ࢨொ֝ඔΓ=∂2f∂S2=∂∆∂SՖࠫޅഈुđΓّ႘ਔ௹ಃࡎ۬აѓ֥ሧӁࡎܱ۬༢౷ཌ֥؇bΓޙਈਔ௹ಃ∆ᆴؓѓ֥ሧӁࡎ۬э߄֥ૹۋ؇đ൞∆֥ૹۋྟᆷѓb࠹ෘᆣಊቆކ֥ΓᆴؓႿส௹Ќᆴ֥ᇗေၩၬᄝႿđޙਈਔ∆ᇏྟЌᆴم֥༂ҵđ༂ҵնཬ౼थႿ௹ಃࡎ۬აѓ֥ሧӁࡎܱ۬༢౷ཌ֥౷؇bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃGamma֥קၬ௹ಃΓקၬ(cont.)ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃGamma֥קၬΓᆴ֥࠹ෘ۴ऌBSM൬ၭሧӁൔ௹ಃקࡎ܄ൔđ൬ၭሧӁुᅨ௹ಃބൔुי௹ಃ֥Γᆴູğ−√1Γ=eSσ2pi(T−t)ః่ࡱཌྷ֥ुᅨ௹ಃაुי௹ಃ֥∆ᆴᆭࡗᆺཌྷҵ၂۱ӈඔđၹՎਆᆀ֥Γᆴሹ൞ཌྷ֥֩b൬ၭሧӁ௹ಃ؟֥Γᆴሹູᆞᆴđ௹ಃॢ֥Γᆴᄵሹູڵᆴb௹ಃ֥Γᆴ္ෛSaraσބT−tэ߄bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃGammaᆴ֥ྟᇉބหᆘΓᆴބѓ֥ሧӁࡎ֥ܱ۬༢֒SᄝXe−(r+σ2)(T−t)ׄൈđΓᆴቋնđ∆ᆴؓႿSቋૹۋbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................௹ಃGammaᆴ֥ྟᇉބหᆘΓᆴބ֞௹௹ཋ֥ܱ༢ࡎ௹ಃॹ֞௹ൈđΓᆴޓնđ∆ᆴؓႿS٤ӈૹۋbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ᆣಊቆކ֥Gammaᆴᆣಊቆކ֥ΓᆴᆺႵ௹ಃႵΓᆴbᆣಊቆކ֥Γᆴ֩Ⴟቆކଽ۲ᇕ௹ಃΓᆴაఃඔਈӰࠒ֥ሹބğ∑nΓ=wiΓii=1ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................GammaᇏྟΓᇏྟᆣಊቆކΓᆴູਬൈӫູԩႿΓᇏྟሑbΓᇏྟ൞ູਔཨԢ∆ᇏྟЌᆴ֥༂ҵđဢ္൞֥ۀbႮႿЌӻΓᇏྟᆺି๙ݖ௹ಃժ֥טᆜࠆ֤đൌགྷΓᇏྟ֥ࢲݔສສ൞∆٤ᇏྟđၹطӈӈߎླေᄎႨѓ֥ሧӁࠇ௹ࠊժࣉྛטᆜđҌି֤ᆣಊቆކൈൌགྷΓᇏྟބ∆ᇏྟbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Gammaᇏྟσ২ğGammaᇏྟࡌഡଖDeltaᇏྟ֥Ќᆴቆކ֥Γᆴ֩Ⴟ−5000đھቆކᇏѓ֥ሧӁ֥ଖ۱ुᅨ௹ಃ؟֥∆ބΓᆴٳљ֩ႿބູЌᆴቆކΓᇏྟđѩЌӻ∆ᇏྟđھቆކႋܓઙ؟ഒٺھ௹ಃđൈછԛ؟ഒٺѓ֥ሧӁĤࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Gammaᇏྟσ২ğGammaᇏྟ(cont.)ھቆކႋܓೆ֥ुᅨ௹ಃඔਈ֩Ⴟğ5000=ܓೆ2500ٺुᅨ௹ಃުđྍቆކ֥∆ᆴࡼႮ0ᄹࡆ֞2500×=2000bၹՎູЌӻ∆ᇏྟđႋԛ൲2000ٺѓ֥ሧӁbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................DeltaaetaބGammaᆭࡗ֥ܱ༢∆aΘބΓᆭࡗ֥ܱ༢Ⴎ൬ၭሧӁ֥ुᅨ௹ಃࡎ۬fડቀ֥BSMັٳٚӱ∂f+∂frS+1σ2S2∂2f∂t∂S2∂S2=rfॖ֤Θ+rS∆+1σ2S2Γ=rf2ھ܄ൔؓ൬ၭሧӁ֥ֆ۱௹ಃބ؟۱௹ಃቆކൡႨbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................DeltaaetaބGammaᆭࡗ֥ܱ༢∆aΘބΓᆭࡗ֥ܱ༢(cont.)ೂݔ∆ᇏྟđΘ+1σ2S2Γ=rf2ؓႿ၂۱∆ᇏྟቆކđΘູڵᆴѩޓնൈđΓࡼ߶ູᆞᆴѩ္ޓնbೂݔ∆ބΓൈᇏྟđΘ=rf∆ᇏྟބΓᇏྟቆކ֥ࡎᆴࡼෛൈࡗၛڄག৵࿃گ০ੱ֥؇ᄹӉbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................DeltaaetaބGammaᆭࡗ֥ܱ༢∆aΘބΓ֥ژݼDeltaetaGamma؟ुᅨ௹ಃ+−+؟ुי௹ಃ−−+ॢुᅨ௹ಃ−+−ॢुי௹ಃ++−ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ଢDeltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴν֥קၬ௹ಃ֥VegačνĎ൞௹ಃࡎ۬ؓѓ֥ሧӁࡎ۬ѯੱσ֥ொ֝ඔν=∂f∂σνޙਈ֥൞௹ಃࡎ۬ؓѓ֥ሧӁࡎ۬ѯੱ֥ૹۋ؇bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴν֥࠹ෘᆣಊቆކ֥νᆴ֩Ⴟھቆކᇏ۲ᆣಊ֥ඔਈა۲ᆣಊ֥νᆴӰࠒ֥ሹބ∑nΓ=wiΓii=1ᆺႵ௹ಃႵνᆴđ௹ಃ؟֥νᆴሹ൞ᆞ֥bؓ൬ၭሧӁुᅨ௹ಃބൔुי௹ಃطđ√ST−−√t·e1ν=2piࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴν֥࠹ෘ(cont.)ႋھᇿၩ֥൞đഈඍνᆴ൞۴ऌBSM௹ಃקࡎ܄ൔෘԛ֥đطᆃਆ۱܄ൔࡌקσູӈඔbၹՎഈඍᆃུ܄ൔႅݣሢᆃဢ֥భิğѯੱູӈඔ౦ঃ༯֥௹ಃࡎ۬აѯੱ൞эਈ౦ঃ༯֥௹ಃࡎ۬൞ཌྷ֥֩bνնཬ౼थႿSaT−tarބσbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴνᆴބѓ֥ሧӁࡎ֥ܱ۬༢ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴνᇏྟቆކ֥νᆴ֩ႿਬൈđᆣಊቆކԩႿνᇏྟሑb֒ૌטᆜ௹ಃժᆣಊቆކԩႿνᇏྟሑൈđྍ௹ಃժ߶ൈڿэᆣಊቆކ֥ΓᆴđၹՎđส௹Ќᆴᆀေᆣಊቆކൈղ֞νᇏྟބΓᇏྟđᇀഒေႨ၂ѓ֥ሧӁ֥ਆᇕ௹ಃb{Γp+Γ1w1+Γ2w2=0νp+ν1w1+ν2w2=0ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴσ২ğGammaᇏྟބVegaᇏྟࡌഡଖ۱ԩႿ∆ᇏྟሑ֥ᆣಊቆކ֥Γᆴູ6000đνᆴູ9000đط௹ಃ1֥Γᆴູđνᆴູđ∆ᆴູ௹ಃ2֥Γᆴູđνᆴູđ∆ᆴູႋӻႵ؟ഒ௹ಃժҌିھቆކԩႿGammaބVegaᇏྟሑĤࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴσ২ğGammaᇏྟބVegaᇏྟ(cont.)۴ऌൔčĎૌႵğ{6000++=09000++=0ࢳᆃ۱ٚӱቆ֤ğw1≈−6522,w2≈−653bၹՎđૌၹࡆೆ6522ٺֻ၂ᇕ௹ಃ֥ॢބ653ٺֻؽᇕ௹ಃ֥ॢҌିھቆކԩႿGammaބVegaᇏྟሑbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................Vegaაส௹Ќᆴσ২ğGammaᇏྟބVegaᇏྟ(cont.)ࡆഈᆃਆᇕ௹ಃժުđྍቆކ֥∆ᆴູ−6522×−653×=−ၹՎಯླઙೆ6262ٺѓ֥ሧӁҌିھቆކԩႿ∆ᇏྟሑbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................rhoაส௹Ќᆴrhoაส௹Ќᆴᆣಊ֥rho֩Ⴟᆣಊࡎ۬ؓ০ੱ֥ொ֝ඔğrho=∂f∂rrhoޙਈ֥൞ᆣಊࡎ۬ؓ০ੱэ߄֥ૹۋ؇bѓ֥ሧӁ֥rhoᆴູ0bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................rhoაส௹Ќᆴrhoაส௹Ќᆴ(cont.)ؓႿ൬ၭሧӁुᅨ௹ಃطđrho=X(T−−r(T−t)t)eN(d2)ؓႿ൬ၭሧӁൔुי௹ಃطđrho=X−r((T−T−t)t)e[N(d2)−1]௹ࠊࡎ֥۬rhoᆴູğrho=(T−t)Fૌॖၛ๙ݖڿэ௹ಃࠇ௹ࠊժটᆣಊቆކԩႿrhoᇏྟሑbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ଢDeltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ࢌၞٮႨაส௹ЌᆴࢌၞٮႨაส௹ЌᆴູਔЌӻᆣಊቆކԩႿ∆aΓaνᇏྟሑđсྶ҂؎טᆜቆކbಖطَ֥טᆜླေնਈ֥ࢌၞٮႨbᄝൌ࠽ᄎႨᇏđส௹Ќᆴᆀ۷ౠཟႿႨ∆aΓaνaΘބrho֩ҕඔটܙఃᆣಊቆކ֥ڄགđಖު۴ऌૌؓSaraσໃটᄎ౦ঃ֥ܙ࠹đॉ੮൞ڎႵсေؓᆣಊቆކࣉྛטᆜbೂݔڄག൞ॖࢤ൳֥đࠇؓሱ࠭Ⴕ০đࣼ҂טᆜĠڄགؓሱ࠭҂০൞҂ॖࢤ൳֥đᄵࣉྛཌྷႋטᆜbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ࢌၞٮႨაส௹Ќᆴσ২ğԚЌᆴᆦԛູਬ֥ส௹ЌᆴҦࡌקᄝ5ᄅٺଖᇕሧӁቆކЇݣ10000ܢAܢௐđሧӁቆކ֥ܵᆀथקࡼAܢௐ֥൧ӆڄགࢆ֮၂϶đࠧေࡼժ֥∆ᆴՖ10000ሇߐӮ5000bࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ࢌၞٮႨაส௹Ќᆴσ২ğԚЌᆴᆦԛູਬ֥ส௹ЌᆴҦ(cont.)ܢௐࡎ۬33ए7ᄅٺ௹ಃ֞௹֥฿ඔ66ڄག০ੱ5%Aܢௐ֥ႅݣѯੱᄅٺ֞௹֥௹ಃ֥ࡎ۬ބ∆ླྀၰࡎູ۬35֥ुᅨ௹ಃ֥ࡎ۬ླྀၰࡎູ۬35֥ुᅨ௹ಃ֥∆ླྀၰࡎູ۬30֥ुי௹ಃ֥ࡎ۬ླྀၰࡎູ۬30֥ुי௹ಃ֥∆−ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ࢌၞٮႨაส௹Ќᆴσ২ğԚЌᆴᆦԛູਬ֥ส௹ЌᆴҦ(cont.)ᄎႨ৳৫ٚӱđૌॖၛԛ௹ಃࢌၞགྷࣁᆦԛູ0֥௹ಃժbॖၛुԛđ܂ૌ࿊ᄴ֥௹ಃᆺႵਆᇕđၹູܢௐ֥∆ູ1đູਔࢆ֮ቆކ֥∆đॖၛܓઙुי௹ಃđൈູਔࢆ֮ЌᆴӮЧđॖၛԛ൲ुᅨ௹ಃটູܓઙुי௹ಃವሧbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ࢌၞٮႨაส௹Ќᆴσ২ğԚЌᆴᆦԛູਬ֥ส௹ЌᆴҦ(cont.)ࡌഡXބYٳљູुᅨ௹ಃބुי௹ಃކჿ֥ٺඔbପહૌ֥ଢѓ൞{ܢௐ֥∆−ुᅨ௹ಃ֥∆+ुי௹ಃ֥∆=5000ઙೆुי௹ಃ֥௹ಃٮᆦԛ−ԛ൲ुᅨ௹ಃ֥௹ಃٮ൬ೆ=0ࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
Deltaა௹ಃ֥ส௹Ќᆴetaაส௹ЌᆴGammaაส௹ЌᆴVegaarhoაส௹ЌᆴࢌၞٮႨაส௹Ќᆴ.........................................................ࢌၞٮႨაส௹Ќᆴσ২ğԚЌᆴᆦԛູਬ֥ส௹ЌᆴҦ(cont.)ࠧ{10000−−=−=0ࢳٚӱॖ֤X=,Y=෮ၛնჿླေ63ٺुᅨ௹ಃބ134ٺुי௹ಃbࣁವ۽ӱCopyright©2009Zheng,Zhenlong&Chen,Rong
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