High accurate modified WENO method for the solution of Black-Scholes equation. (English) Zbl 1314.91238
Summary: 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 nonlinear Black-Scholes equation is demonstrated numerically. Comparisons are made with the available methods in the literature.
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35A35 | Theoretical approximation in context of PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
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