Finite element solutions of the nonlinear RAPM Black-Scholes model

2021/03/15 by Wei, Dongming, Erlangga, Yogi Ahmad, Pak, Andrey +1
#65M22 #65M60 #91G60 #Computational Finance (q-fin.CP) #FOS: Economics and business

paper · doi:10.48550/arxiv.2103.08380

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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