Collocation method based on modified ‎cubic‎ B-spline ‎for option pricing ‎models

Jalil Rashidinia; Sanaz Jamalzadeh

Vol. 22 No. 1 (2017)

Regular Articles

Collocation method based on modified ‎cubic‎ B-spline ‎for option pricing ‎models

Published 2016-10-17

Jalil Rashidinia
Sanaz Jamalzadeh

Jalil Rashidinia
Department of Mathematics, Iran University of Science and Technology

Sanaz Jamalzadeh
Department of Mathematics, Iran University of Science and Technology

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Abstract

Collocation‎‎ ‎method ‎based ‎on ‎modified‎ cubic B-spline functions ‎has ‎been ‎developed‎ ‎for ‎the ‎valuation ‎‎‎of European‎, ‎American and Barrier options of single ‎asset. ‎The ‎new ‎approach ‎contains ‎‎discretizing ‎of‎ t‎‎emporal ‎derivative‎ ‎using ‎finite ‎difference ‎approximations ‎and ‎approximating‎ the option price with the ‎modified‎ B-spline functions‎. ‎Stability of this method has been discussed and shown that it is unconditionally stable‎. ‎The ‎efficiency ‎of ‎the‎ ‎proposed ‎method ‎is ‎tested ‎by ‎different ‎examples‎‎‎.‎

Keywords

Options ‎Pricing, ‎ Redefined Cubic B-‎spline, ‎ Stability

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