| Home  | About ScienceAsia  | Publication charge  | Advertise with us  | Subscription for printed version  | Contact us  
Editorial Board
Journal Policy
Instructions for Authors
Online submission
Author Login
Reviewer Login
Volume 50 Number 2
Volume 50 Number 1
Volume 49 Number 6
Volume 49 Number 5
Volume 49S Number 1
Volume 49 Number 4
Earlier issues
Volume 49 Number 3

Research articles

ScienceAsia 50 (2024):ID 2024035 1-7 |doi: 10.2306/scienceasia1513-1874.2024.035

Numerical simulation of a nonlinear model in finance by Broyden?s method

Xianfu Zenga, Hongwei Liub, Haiyan Songc,*

ABSTRACT:     In this paper, we study the stationary Black-Scholes model arising in finance with transaction costs. This model becomes interesting when the time does not play a role such as, for instance, in perpetual options. The equation describing this model is a nonlinear second-order boundary value problem and there is no analytic solutions in closed form for such a nonlinear equation. After discretization via the centered finite difference formula we have to solve a nonlinear algebraic system which would be a serious problem when we use a small discretization mesh. We solve this nonlinear system by the residual-based Broyden?s method, which is an efficient quasi-Newton method and is convenient to implement by a desk computer. We give a convergence analysis of the Broyden?s method by assuming a lower and upper bound of the converged solution of the Black-Scholes model. Numerical results are given to show that the convergence rate of the method is robust with respect to the discretization mesh and the problem parameters.

Download PDF

0 Downloads 141 Views

a College of International Economics and Trade, Ningbo University of Finance and Economics, Ningbo 315175, Zhejiang, China
b School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China
c School of Computer and Data Engineering, NingboTech University, Ningbo 315100, Zhejiang, China

* Corresponding author, E-mail: haiyansong@nbt.edu.cn

Received 12 Jan 2023, Accepted 21 Jan 2024