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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.
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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