An efficient nonstandard numerical method with positivity preserving property

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چکیده مقاله:

Classical explicit finite difference schemes are unsuitable for the solution of the famous Black-Scholes partial differential equation, since they impose severe restrictions on the time step. Furthermore, they may produce spurious oscillations in the solution. We propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. The proposed method is constructed based on a nonstandard discretization of the spatial derivatives and is applicable to Black-Scholes equation in the presence of discontinues initial conditions.

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عنوان ژورنال

دوره 4  شماره 2

صفحات  161- 169

تاریخ انتشار 2016-10-29

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