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arXiv · 2409.01125

IMEX-RK finite volume methods for nonlinear 1d parabolic PDEs. Application to option pricing

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

The goal of this paper is to develop 2nd order Implicit-Explicit Runge-Kutta (IMEX-RK) finite volume (FV) schemes for solving 1d parabolic PDEs for option pricing, with possible nonlinearities in the source and advection terms. The spatial semi-discretization of the advection is carried out by combining finite volume methods with 2nd order state reconstructions; while the diffusive terms are discretized using second-order finite differences. The time integration is performed by means of IMEX-RK time integrators: the advection is treated explicitly, and the diffusion, implicitly. The obtained numerical schemes have several advantages: they are computationally very efficient, thanks to the implicit discretization of the diffusion in the IMEX-RK time integrators, which allows to overcome the strict time step restriction; they yield second-order accuracy for even nonlinear problems and with non-regular initial conditions; and they can be extended to higher order.

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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. IMEX-RK finite volume methods for nonlinear 1d parabolic PDEs. Application to option pricing. https://doi.org/10.1007/978-3-031-55264-9_36

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