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A finite element approach to the numerical solutions of Leland’s model

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  • Wei, Dongming
  • Erlangga, Yogi Ahmad
  • Zhumakhanova, Gulzat

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 favourably with the finite difference results in the literature for the model.

Suggested Citation

  • Wei, Dongming & Erlangga, Yogi Ahmad & Zhumakhanova, Gulzat, 2024. "A finite element approach to the numerical solutions of Leland’s model," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 582-593.
    • Handle: RePEc:eee:reveco:v:89:y:2024:i:pa:p:582-593
    DOI: 10.1016/j.iref.2023.07.076
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