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Finite element solutions of the nonlinear RAPM Black-Scholes model

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  • Dongming Wei
  • Yogi Ahmad Erlangga
  • Andrey Pak
  • Laila Zhexembay

Abstract

his paper presents finite element methods for solving numerically the Risk-Adjusted Pricing Methodology (RAPM) Black-Scholes model for option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are formulated using some group finite elements and numerical quadrature to handle the nonlinear term, in combination with a Crank-Nicolson-type temporal scheme. The temporal scheme is implemented using the Rannacher approach. 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.

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  • Dongming Wei & Yogi Ahmad Erlangga & Andrey Pak & Laila Zhexembay, 2021. "Finite element solutions of the nonlinear RAPM Black-Scholes model," Papers 2103.08380, arXiv.org.
    • Handle: RePEc:arx:papers:2103.08380
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    File URL: http://arxiv.org/pdf/2103.08380
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