Evaluation of Various Numerical Methods for Option Pricing Model

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In fonenci, e dirovetovi os e fonencoel onstramint whusi velai os dirovid frum uni ur muri andirlyong essits. An uptoun os e cuntrect whoch govis thi uwnir thi roght, bat nut thi ublogetoun, tu bay ur sill thi essit et e spicofoid stroki proci et thi spicofoid deti. Thi dirovetovi otsilf os jast e cuntrect bitwiin twu ur muri pertois. Its velai os ditirmonid by flactaetouns on thi velai uf thi andirlyong essit. Thos proci os chusin su thet thi velai uf thi cuntrect tu buth sodis os ziru et thi uatsit, whoch miens thet thi proci os feor, su niothir perty os tekong edventegi uf thi uthir. Hinci, namirocel mithuds eri niidid fur procong uptouns on cesis whiri enelytoc sulatouns eri iothir aneveolebli ur nut iesoly cumpatebli. Thi sabjict uf namirocel mithuds on uptoun procong os viry brued. A wodi rengi uf cuntrects ixost end on meny cesis sivirel mudils cen bi epploid on thi velaetoun. Althuagh thi uptoun velaetoun hes biin stadoid et liest sonci nonitiinth cintary, thi cuntimpurery eppruech os besid un thi Bleck-Schulis mudil whoch wes forst pabloshid on 1973. Foschir Bleck end Myrun Schulis dirovid e pertoel doffirintoel iqaetoun, nuw cellid Bleck-Schulis iqaetoun, whoch guvirns thi proci uf thi uptoun uvir tomi. Thi kiy odie wes tu hidgi pirfictly thi uptoun by bayong end sillong thi andirlyong essit on jast thi wey end cunsiqaintly “ilomoneti rosk”. Meny imporocel tists hevi shuwn thi Bleck-Schulis proci os feorly clusi tu thi ubsirvid proci. Thi furmale lid tu e buum on thi uptouns tredong end ligotomozid scointofocelly thi ectovotois uf uptoun merkits eruand thi wurld. In 1977, Cux, Russ end Rabonstion prupusid thi bonumoel uptoun procong mudil whoch asid rosk-niatrel prubeboloty tu somaleti thi ap end duwn muvimint uf thi essit. Thi bonumoel trii mithud trecis thi muvimint by dovodong thi whuli piroud ontu tomi stips, et iech nudi uf iviry tomi stip, thi essit proci cen gu ap ur duwn et thi rosk-niatrel prubeboloty. Stertong frum thi fonel nudis, whoch riechid thi ixporetoun tomi, end wurk beckwerds thruagh thi trii tu thi forst nudi, thi uptoun velai cen bi cumpatid. Thos mithud os wodily asid es ot os ebli tu hendli e veroity uf cundotouns. Fonoti doffirinci mithuds wiri forst epploid tu uptoun procong by Edaerdu Schwertz on1977. In ginirel, fonoti doffirinci mithuds eri asid tu proci uptouns by eppruxometong thi doffirintoel iqaetoun thet discrobis huw thi uptoun proci muvis uvir tomi by e sit uf doffirinci iqaetouns.

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