
puttu-kooll thulyatha

saambathika ganithashaasthrathil, puttu-kooll paarity oru europian kooll oopshanteyum europian puttu oopshanteyum vila thammilulla bandhathe nirvachikkunnu, ore strike prise kaalaharanavum ulla, athaayath oru long kooll oopshanteyum short puttu oopshanteyum portfolio eee strike prisilum kaalaharanapedalilum orotta forwade kararinu thulyamaanu (athinaal ithinu athe moolyamundu). kaalaharanappedunna vila strike prisinu mukalilaanenkil, kooll prayogikkum, athesamayam athu thaazheyaanenkil, puttu prayogikkum, athinaal rund saahacharyangalilum aasthiyude oru yoonit strike prisinu vaangum, oru forwade karaarilennapole.
eee bandhatthinte saadhuthaykk chila anumanangal thripthippedendathundu; iva vyakthamaakkukayum bandham chuvade uruthirinjirikkunnu. praayogikamaayi edapaadu chelavukalum dhanakaarya chelavukalum (liverage) ardhamaakkunnathu eee bandham krithyamaayi nilanilkkilla, pakshe draavaka vipanikalil bandham krithyathayodu aduthaanu.
anumanangal.
puttu-kooll paarity oru staatik replicationaanu, athinaal oru forwade karaarinte nilanilpp enna kuranja anumanangal aavasyamaanu. trade cheytha forwade karaarukalude abhaavathil, forwade karaarine adisthaana aasthi vaangaanum nischitha kaalayalavilekku kadam vaangunnathiloode (udha.jii.bondukal kadamedukkuka), allengil adisthaana aasthi kadam vaangukayum vilkkukayum cheyyuka (hrasvamaayi), koodaathe labhicha panam kaalaavadhikkaayi vaaypa nalkuka, rund saahacharyangalilum oru svayam dhanakaarya portfolio nalkunnu.
eee anumaanangalkk prarambha theeyathiyum kaalaharanavum thammilulla edapaadukalonnum aavasyamilla, athinaal black-schole modaline apekshichu avaa valare durbalamaanu, ithinu chalanathmakamaaya replication adisthaanathilulla thudarchayaaya edapaadukalum aavasyamaanu.
oraalkk derivative edapaadukalil praveshikkaan kazhiyumennu replication anumaanikkunnu, athinu liverage aavasyamaanu (ithinu mooladhana chelavukalum aavasyamaanu), koodaathe vaangunnathinum vilkkunnathinum edapaadu chelavukal, prathyekichu lelam-chodikkal vyaapanam ulppedunnu. athinaal eee bandham paridhiyillaattha panalabhyathayulla anuyojyamaaya gharshanarahita vipaniyil maathrame nilanilkkoo. ennirunnaalum, yadhaartha loka vipanikal krithyamaaya bandhathinu aduthullathra draavakamaayirikkaam, pradhana karansikaliloo pradhana stokku soochikakalilo efx vipanikal, vipani prakshubdhathayude abhaavathil.
prasthavana.
puttu-kooll thulyatha niravadhi thulyamaaya reethikalil prasthaavikkam, ettavum kaduppameriya reethiyil
formula _ 1 ennathu oru kolinte (nilavile) moolyamaanu, formula _ 2 ennathu oru puttinte (nilavile) moolyamaanu, formula _ 3 ennathu kizhivu gadakamaanu, formula _ 4 ennathu adisthaana aasthiyude forwade vilayaanu, formula _ 5 ennathu strike prais aanu. idathu vasham oru neenda kolinteyum hraswa puttinteyum portfoliyoyumaayi poruthappedunnu; valath vasham oru forwade karaarumaayi poruthappedunnu. idathu vashathulla asattu formula 1, formula 2 enniva varthamaana moolyangalil nalkiyirikkunnu, athesamayam asattu formula 4, formula 5 enniva bhaavi moolyangalil nalkiyirikkunnu (aasthiyude forwade vila, kaalaharanappedumbol nalkunna strike vila), ithu discound factor formula 3 varthamaana moolyangalilekku parivartthanam cheiyunnu.
ippol forwade prais formula formula 3 upayogichu forwade prais formula ninnu kizhivu nalkikkond spott prais formula 11 labikkum. forwade prais formula 4 nuu pakaram spott prais formula 14 upayogichu namukk nalkunnu
nibandhanakal punakrameekarikkunnath oru aadya vyaakhyaanam nalkunnu
ivide idathu vashath oru fiduciary kooll undu, ithu oru neenda kolum strike prais nalki athu prayogikkaan mathiyaya panavum (allengil bondukal) aanu. valathuvashath oru vivahita puttu aanu, ithu aasthiyumayi jodiyakkiya oru neenda puttu aanu, athinaal vyayaamam cheyyumbol swath strike vilaykk wilkan kazhiyum. kaalavadhi theerumbol, oopshanukalude aantharika moolyam aprathyakshamaakunnu, athinaal irupakshathinum kuranjathu strike prais formula 5 allengil aasthiyude moolya formula 14 nuu thulyamaaya payy oof formula 16 undu.
panathodulla oru neenda kooll aasthiyodulla oru neenda nikshepathinu thulyamaanu ennathu puttu-kooll thulyathayude oru ardhamaanu.
padangal mattoru reethiyil punakrameekarikkunnath namukk randaamathe vyaakhyaanam nalkunnu
ippol idathu vashath oru kyash secured puttu aanu, athaayath, oru short puttu, avar athu upayogichaal puttu udamaykku nalkaan mathiyaya panam. valathuvashath oru covered kooll aanu, ithu aasthiyumayi jodiyakkiya oru hraswa kooll aanu, avide kooll udama athu prayogichaal vilikkaan thayyaaraan. kaalavadhi theerumbol, munkaala sahacharyam flip cheyyappedunnu. irupakshathinum ippol strike prais formula 5 allengil aasthiyude moolya formula 14 nuu thulyamaaya payment formula 19 undu, eathaanu "kuravu".
athinaal puttu-kooll thulyathaye kyash-secured (short) puttu, covered (short) kooll ennivayude thulyathayaayi manassilakkaanum kazhiyumennu nammal kaanunnu. oru surakshithamaaya panam vilkkunnath oru covered kooll vilkkunnathinekkaal apakadakaramaanennu saadhaaranayaayi kaanappedunnathinal ithu athishayakaramaan.
panatthinte samaya moolyavum saambathika veriyabilukalude samayathe ashrayikkunnathum vyakthamaakkunnathin, yadhaartha puttu-kooll paarity samavaakyam ingane prasthaavikkam
evide
samavaakyathinte valathuvashath delivari prais formula _ 5 ulla stokkil oru forwade karar vaangunnathinulla vilayum undennu shradhikkuka. athinaal samavaakyam vaayikkanulla oru maarggam neelamulla oru kolum hrasvamaaya oru puttum ulla oru portfolio deerghamaaya oru forwade aayirikkunnathin thulyamaanu ennathaanu. prathyekichum, adisthaanamaayathu trade cheyyaavunnillenkil athil forwadeukal undengil, namukk valathuvashathe expressione forvedinte vila upayogichu maattisthaapikkaam.
boond palisha nirakk, formula _ 31, sthiramaanennu karuthukayaanengil
kurippu formula _ 31 ennathu palisha sakthiye soochippikkunnu, ithu cheria palisha nirakkukalude phalapradamaaya vaarshika nirakkin ekadesham thulyamaanu. ennirunnaalum, oraal ekadesha kanakk shradhikkanam, prathyekichu valia nirakkukalum valia samaya kaalayalavukalum. formula _ 31 krithyamaayi kandethunnathinu, formula _ 34 upayogikkuka, ivide formula _ 35 phalapradamaaya vaarshika palisha nirakkaanu.
stokkukalil ezhuthiyirikkunna europian oopshanukal vilayiruthaan, oopshante aayussil nalkunna ariyappedunna labhavihitam, formula ithaayirikkum
formula _ 36 ennathu oru stokku shareil ninnulla laabhavihithathinte motham moolyathe prathinidheekarikkunnu, oopshanukalude sheshikkunna kaalayalavil nalkendathaanu, nilavile moolyathilekku kizhivu.
namukk samavaakyam ingane mattiyezhuthaam
delivari prais formula _ 5 ulla stokkile oru forwade karaarinte vilayaanu valathuvashath ennathu shradhikkuka.
derivation.
puttu aandu kooll oopshanukal trade cheytha stokkukalilaanennu nammal karuthunnu, ennaal adisthaanaparamaayi mattethenkilum trade cheyyaavunna asattu aakam. thaazhepparayunna "noow arbitrage" vaadathinu adisthaanamaayathu vaangaanum vilkkanumulla kazhivu nirnaayakamaan.
aadyam, arbitrage avasarangalonnumillenna anumaanathinu keezhil (vilakal arbitrage rahithamaan), ellaayppozhum ore prathifalamulla rund portfoliyokalkku eathu samayathum ore moolyam undaayirikkanam. ithu theliyikkaan, "tii" kku munbulla chila samayangalil, oru portfolio mattethinekkaal vilakuranjathaanennu karuthuka. appol oraalkk vilakuranja portfolio vaangaanum (deerghaneram) kooduthal chelaveria vilkkanum (hrasvamaayi) kazhiyum. tii" samayat, njangalude mothatthilulla portfolioykku, ohari vilayude eathu moolyathinum poojya moolyamundaakum (ellah aasthikalum baadhyathakalum raddaakkappettu). tii" samayat naam nediya labham apakadasaadhyathayillaatha laabhamaan, pakshe ithu oru madhyasthathayumillenna nammude anumaanathe lamghikkunnu.
ore prathifalamulla (staatik replication) rund portfoliyokal srishtikkukayum melpparanja thathwam (yukthisahamaya vilanirnayam) abhyarthikkukayum cheythukondu njangal puttu-kooll paarity bandham nedum.
labhavihitam nalkaatha chila stokkukalil athe theeyathiyil "tii" kaalaharanappedunnathin ore strike "keey" ulla oru kooll oopshanum puttu oopshanum pariganikkuka. maturity samayat 1 dollar nalkunna oru bondinte asthithvam nammal anumaanikkunnu. boond vila kramarahithamayirikkaam (stokku pole) pakshe maturity samayat 1 nuu thulyamayirikkanam.
t samayat "s"-nte vila s (t) ayirikkatte. ippol oru kooll oopshan "sii" vaangi athe maturity "tii", strike "keey" ennivayude puttu oopshan "pii" vitt oru portfolio kootticherkkuka. eee portfoliyoyude prathiphalam "s (t)-k" aanu. ippol oru ohari vaangukayum "keey" bondukal kadam vaangukayum cheythukondu randaamathe portfolio kootticherkkuka. s (t)" ennathinu vangiya nammude ohari "s (t)" ennathinu thulyavum kadam vangiya bondukal "k" ennathinu thulyavumayathinaal, randaamathe portfoliyoyude prathiphalavum "s (t)-k" "t" aanu.
rund portfoliyokalkkum pothuvaaya samaya soothravaakyathil ore vila undaayirikkanamennu ore prathiphalangal soochippikkunnuvenna njangalude praadhamika nireekshanatthiloode, vividha upakaranangalude moolyam thammil inipparayunna bandham nilanilkkunnu
athinaal arbitrage avasarangalonnum labhikkathathinaal, puttu-kooll paarity ennariyappedunna melpparanja bandham nilanilkkunnu, koodaathe kooll, puttu, boond, stokku ennivayude eathenkilum moonnu vilakalkku oraalkk naalaamathethinte soochippicha vila kanakkakkaan kazhiyum.
laabhavihithangalude kaaryatthil, parishkkaricha formula mukalil paranjathinu samanamaaya reethiyil uruthirinjekkaam, ennaal oru portfoliyoyil oru kooll dairkhyameriyathum, oru puttu short cheiyunnathum, oororutharum maturity samayat 1 dollar nalkunna "dii (tii)" bondukalum ulppedunna parishkkaranatthode (bondukalkku "tii" samayat "dii (tii)" moolyam varum); mattu portfolio munbatheppole thanneyaanu-stokkinte oru ohari dairkhyameriyathum, oororutharum "tii" yill 1 dollar nalkunna hraswa "keey" bondukalum. vyathyasam enthennaal, "tii" samayat, stokku "ezz (tii)" ennathinu mathramalla, dividandaayi "dii (tii)" nalkukayum cheythu ennathaanu.
charithram.
puttu-kooll samaanathayude roopangal madhyakaalakhattathil thanne praayogikamaayi prathyakshappettu, irupathaam noottaandinte thudakkathil niravadhi ezhuthukaar ithu aupachaarikamaayi vivarichu.
aadhunika saambathika naveekaranatthinte purathana verukal niyanthrana vyavahaarathinte aadyakaala charithram" enna grandhatthil maikkal noll, madhyakala englandil oru aadhunika panayamvekkunnathinte nirvachikkunna swabhaavamaaya veendedukkalinte thulyatha vikasippikkunnathil puttu-kooll paarity vahicha pradhana punk vivarikkunnu.
pathonpathaam noottaandil, dhanakaarya vidagthanaaya russell sej synthetic vaaypakal srishtikkaan puttu-kooll paarity upayogichu, akkaalathe palisha niyamangal saadhaaranayaayi anuvadikkunnathinekkaal uyarnna palisha nirakkukalundaayirunnu.
newyorkkile oru oopshan arbitrage vyaapaariyaaya nelson oru pusthakam prasidheekarichu "dhii eiii.bii.sii. 1904-leeii oopshanukalum arbitrage puttu-kooll thulyathaye vishadamaayi vivarikkunnu. 2000-kalude thudakkathil espen garder hagg addehathinte pusthakam veendum kandethukayum nelsante pusthakatthil ninnulla niravadhi paraamarshangal haaginte "derivative modalukal oonn modalukal" enna pusthakatthil nalkukayum cheythu.
1910-leeii puttu-kooll thulyathaye henry dutch thante "arbitrage inn bullian, nanayangal, billukal, stokkukal, shareukal, oopshanukal, randaam pathipp" enna pusthakatthil vivarikkunnu. landan engham vilson ennaal nelsonekkaal vishadaamshangal kuravaanu (1904).
ganithashaasthra professor winsense bronsinum 1908 ll puttu-kooll paarity nedukayum vyathyastha vitharanagalude oru parambaraykku keezhil ganithashaasthra oopshan modalukalude oru parambara vikasippikkunnathin thante arbitrage vaadathinte bhaagamaayi ithu upayogikkukayum cheiyunnu. professor bronsinte pravartthanangal aduthide professor wolfgang haffner professor hains simmerman veendum kandethi. jarmman bhashayil ezhuthiya oru pusthakamaanu bronsinte yadhaartha kruthi, ippol haffner simmerman ("winsense bronsinte oopshan prising modalukal", springer verlag) edittu cheytha oru kruthiyil engleeshil vivarthanam cheyyukayum prasidheekarikkukayum cheiyunnu.
aadhunika academic saahithyathile athinte aadya vivaranam hans aarr aanu. jenal oof financil" stool cheyyuka. 
prathyaaghaathangal.
puttu-kooll thulyatha soochippikkunnathu