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A robust and accurate finite difference method for a generalized Black-Scholes equation. (English) Zbl 1214.91130
Summary: We present a numerical method for a generalized Black-Scholes equation, which is used for option pricing. The method is based on a central difference spatial discretization on a piecewise uniform mesh and an implicit time stepping technique. Our scheme is stable for arbitrary volatility and arbitrary interest rate, and is second-order convergent with respect to the spatial variable. Furthermore, the present paper efficiently treats the singularities of the non-smooth payoff function. Numerical results support the theoretical results.
MSC:
91G60Numerical methods in mathematical finance
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M50Mesh generation and refinement (IVP of PDE)
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