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

Author

Listed:
  • Dongming Wei
  • Yogi Ahmad Erlangga
  • Gulzat Zhumakhanova

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.

Suggested Citation

  • Dongming Wei & Yogi Ahmad Erlangga & Gulzat Zhumakhanova, 2020. "A Finite Element Approach to the Numerical Solutions of Leland's Mode," Papers 2010.13541, arXiv.org.
    • Handle: RePEc:arx:papers:2010.13541
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    2. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
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