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

2020/10/26 by Dongming Wei, Wei, Dongming, Yogi A. Erlangga +4 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #65M22 #65M60 #91G60 #Computational Finance (q-fin.CP) #Differential Equations and Numerical Methods #FOS: Economics and business #Fluid Dynamics and Turbulent Flows #Stochastic processes and financial applications #msc:65M22 #msc:65M60 #msc:91G60 #q-fin.CP

paper · pdf · doi:10.48550/arxiv.2010.13541

13 pages, 8 figures

arxiv created 2020/10/26 · openalex publication_date 2020/10/26 · arxiv updated 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Pricing of Options and Corporate Liabilities

Cited by

• Finite element solutions of the nonlinear RAPM Black-Scholes model

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