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A new higher order compact finite difference method for generalised Black–Scholes partial differential equation: European call option

Publication Type : Journal Article

Publisher : North-Holland

Source : North-Holland

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2020

Abstract : This paper presents a high order numerical method based on a uniform mesh to obtain a highly accurate result for generalized Black–Scholes equation arising in the financial market. We first semi-discretize the underlying problem in the temporal direction by using Crank–Nicolson scheme and then discretize the resulting set of equations by using a high order compact finite difference method (HOCFDM). The stability of the scheme is analyzed. Convergence of the suggested method is proved. It is shown that the method is of order O (Δ t 2+ h 4). Some numerical experiments are carried out in order to illustrate the applicability and accuracy of the proposed method and to validate the theoretical results as well. It is shown that HOCFDM solution matches very well with the exact solution. Further, the rate of convergence predicted theoretically is the same as that obtained numerically.

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