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Mathematics > Numerical Analysis

arXiv:2409.01125 (math)
[Submitted on 2 Sep 2024 ]

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

Title: IMEX-RK 有限体积方法用于非线性一维抛物型偏微分方程 应用到期权定价

Authors:J. G. López-Salas, M. Suárez-Taboada, M. J. Castro, A. M. Ferreiro-Ferreiro, J. A. García-Rodríguez
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.
Subjects: Numerical Analysis (math.NA) ; Analysis of PDEs (math.AP)
Cite as: arXiv:2409.01125 [math.NA]
  (or arXiv:2409.01125v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2409.01125
Journal reference: López-Salas, J.G. et. al. IMEX-RK Finite Volume Methods for Nonlinear 1d Parabolic PDEs. Application to Option Pricing. In: Hyperbolic Problems: Theory, Numerics, Applications. SEMA SIMAI Springer Series, vol 35. Springer, Cham, 2024
Related DOI: https://doi.org/10.1007/978-3-031-55264-9_36

Submission history

From: José Germán López-Salas [view email]
[v1] Mon, 2 Sep 2024 10:01:10 UTC (227 KB)
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