Adv. Appl. Math. Mech., 11 (2019), pp. 535-558.
Published online: 2019-01
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A new numerical method is proposed and investigated for solving two- dimensional Black-Scholes option pricing model. This model is represented by Dirichlet initial-boundary value problem in a rectangular domain for a parabolic equation with advection-diffusion operator containing mixed derivatives. It is approximated by using a finite element method in spatial variables and alternating direction implicit (ADI) method in time variable. The ADI scheme is based on the semi-implicit approximation. The stability and convergence of the constructed scheme is proved rigorously. The provided computational results demonstrate the efficiency and high accuracy of the proposed method.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0144}, url = {http://global-sci.org/intro/article_detail/aamm/12976.html} }A new numerical method is proposed and investigated for solving two- dimensional Black-Scholes option pricing model. This model is represented by Dirichlet initial-boundary value problem in a rectangular domain for a parabolic equation with advection-diffusion operator containing mixed derivatives. It is approximated by using a finite element method in spatial variables and alternating direction implicit (ADI) method in time variable. The ADI scheme is based on the semi-implicit approximation. The stability and convergence of the constructed scheme is proved rigorously. The provided computational results demonstrate the efficiency and high accuracy of the proposed method.