Translator Disclaimer
2009 On the consistency of finite difference approximations of the Black–Scholes equation on nonuniform grids
Myles Baker, Daniel Sheng
Involve 2(4): 479-494 (2009). DOI: 10.2140/involve.2009.2.479

Abstract

The Black–Scholes equation has been used for modeling option pricing extensively. When the volatility of financial markets creates irregularities, the model equation is difficult to solve numerically; for this reason nonuniform grids are often used for greater accuracy. This paper studies the numerical consistency of popular explicit, implicit and leapfrog finite difference schemes for solving the Black–Scholes equation when nonuniform meshes are utilized. Mathematical tools including Taylor expansions are used throughout our analysis. The consistency ensures the basic reliability of the finite difference schemes based on choices of temporal and variable spatial derivative approximations. Truncation error terms are derived and discussed, and numerical experiments using C, C++ and Matlab are given to illustrate our discussions. We show that, though orders of accuracy are lower compared with their peers on uniform grids, nonuniform algorithms are easy to implement and use for turbulent financial markets.

Citation

Download Citation

Myles Baker. Daniel Sheng. "On the consistency of finite difference approximations of the Black–Scholes equation on nonuniform grids." Involve 2 (4) 479 - 494, 2009. https://doi.org/10.2140/involve.2009.2.479

Information

Received: 4 June 2009; Revised: 23 July 2009; Accepted: 27 July 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1182.91193
MathSciNet: MR2579565
Digital Object Identifier: 10.2140/involve.2009.2.479

Subjects:
Primary: 65G50, 65L12, 65N06, 65N15
Secondary: 65D25, 65L70, 65L80

Rights: Copyright © 2009 Mathematical Sciences Publishers

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.2 • No. 4 • 2009
MSP
Back to Top