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arXiv · 2409.01131

Second order finite volume IMEX Runge-Kutta schemes for two dimensional parabolic PDEs in finance

J. G. López-Salas·M. Suárez-Taboada·M. J. Castro·A. M. Ferreiro-Ferreiro·J. A. García-Rodríguez
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Abstract

We present a novel and general methodology for building second-order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two-dimensional financial parabolic PDEs with mixed derivatives. The methods achieve second-order convergence even in the presence of non-regular initial conditions. The IMEX time integrator allows to overcome the tiny time-step induced by the diffusive term in the explicit schemes, also providing accurate and non-oscillatory approximations of the Greeks.

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J. G. López-Salas, M. Suárez-Taboada, M. J. Castro, A. M. Ferreiro-Ferreiro, J. A. García-Rodríguez. 2024-09-02. Second order finite volume IMEX Runge-Kutta schemes for two dimensional parabolic PDEs in finance. https://doi.org/10.1007/978-3-031-55264-9_13

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