IMEX-RK Finite Volume Methods for Nonlinear 1d Parabolic PDEs. Application to Option Pricing
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IMEX-RK Finite Volume Methods for Nonlinear 1d Parabolic PDEs. Application to Option PricingAutor(es)
Fecha
2024-06-06Cita bibliográfica
López-Salas, J.G., Suárez-Taboada, M., Castro, M.J., Ferreiro-Ferreiro, A.M., García-Rodríguez, J.A. (2024). IMEX-RK Finite Volume Methods for Nonlinear 1d Parabolic PDEs. Application to Option Pricing. In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-031-55264-9_36
Resumen
[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, that 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.
Palabras clave
Finite volume
IMEX
Mathematical finance
IMEX
Mathematical finance
Descripción
The conference was held in Málaga, Spain, June 20-24, 2022. ©2024 This version of the article has been accepted for publication, after
peer review and is subject to Springer Nature’s AM terms of use, but is not
the Version of Record and does not reflect post-acceptance improvements,
or any corrections. The Version of Record is available online at:
https://doi.org/10.1007/978-3-031-55264-9_36
Versión del editor
ISSN
2199-3041
2199-305X
2199-305X
ISBN
978-3-031-55263-2 978-3-031-55266-3 978-3-031-55264-9