Original scientific paper
https://doi.org/10.64785/mc.30.2.4
An efficient robust computational method for solving Black-Scholes PDEs
Saurabh Bansal
orcid.org/0000-0002-7798-3290
; Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati , India
*
Natesan Srinivasan
* Corresponding author.
Abstract
In this article, we propose a computational method for the numerical solution of Black-Scholes PDEs arising in option pricing. First, we discretize the time-domain by uniform mesh and apply the Crank-Nicolson method to approximate the time variable. Then, we use the streamline-diffusion finite element method (SDFEM) for the spatial derivative on different nonuniform meshes. The proposed method is of second-order convergent in both variables. For comparison purposes, we use the backward-Euler scheme for the time derivative, which will be of first-order convergent. Numerical experiments are carried out to verify theoretical results.
Keywords
option pricing; Black-Scholes equation; streamline-diffusion finite element method; butterfly option
Hrčak ID:
335665
URI
Publication date:
22.9.2025.
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