A Finite Element Approach to the Numerical Solutions of Leland's Mode

Author First name, Last name, Institution

Dongming Wei, Nazarbayev University
Yogi Erlangga, Zayed UniversityFollow
Gulzat Zhumakhanova, Nazarbayev University

Document Type

Article

Source of Publication

arXiv: Computational Finance

Publication Date

10-26-2020

Abstract

In this paper, finite element method is applied to Leland's model for numerical simulation of option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are formulated in combination with a Crank-Nicolson-type temporal scheme. The temporal scheme is implemented using the Rannacher approach. Examples with several sets of parameter values are presented and compared with finite difference results in the literature. Spatial-temporal mesh-size ratios are observed for controlling the stability of our method. Our results compare favorably with the finite difference results in the literature for the model.

Disciplines

Computer Sciences | Physical Sciences and Mathematics

Recommended Citation

Wei, Dongming; Erlangga, Yogi; and Zhumakhanova, Gulzat, "A Finite Element Approach to the Numerical Solutions of Leland's Mode" (2020). All Works. 96.
https://zuscholars.zu.ac.ae/works/96

Indexed in Scopus

no

Open Access

no