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- Title
High accurate modified WENO method for the solution of Black-Scholes equation.
- Authors
Hajipour, Mojtaba; Malek, Alaeddin
- Abstract
In this paper, we propose a high accurate method based on non-standard Runge-Kutta (NRK), modified weighted essentially non-oscillatory (MWENO) and grid stretching methods to solve the Black-Scholes equation with discontinuous final condition. For the spatial and temporal discretization of the Black-Scholes equation, the MWENO method and the NRK method are applied, respectively. The MWENO method is a high-order method that prevents the appearance of spurious solutions close to non-smooth points. To achieve the high-order accuracy in non-smooth points as well as smooth points, a grid stretching technique is employed. The accuracy analysis and the CFL stability condition of this hybrid method are presented. The high efficiency of this method for the solution of non-linear Black-Scholes equation is demonstrated numerically. Comparisons are made with the available methods in the literature.
- Subjects
BLACK-Scholes model; RUNGE-Kutta formulas; NUMERICAL solutions to equations; DISCONTINUOUS functions; SMOOTHING (Numerical analysis)
- Publication
Computational & Applied Mathematics, 2015, Vol 34, Issue 1, p125
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-013-0108-5