A second order finite volume IMEX Runge-Kutta scheme for two dimensional PDEs in finance

J. G. L\'opez-Salas, M. Su\'arez-Taboada, M. J. Castro, A. M. Ferreiro-Ferreiro and J. A. Garc\'ia-Rodr\'iguez

Papers from arXiv.org

Abstract: In this article we present a novel and general methodology for building second order finite volume implicit-explicit (IMEX) numerical schemes for solving two dimensional financial parabolic PDEs with mixed derivatives. In particular, applications to basket and Heston models are presented. The obtained numerical schemes have excellent properties and are able to overcome the well-documented difficulties related with numerical approximations in the financial literature. The methods achieve true second order convergence with non-regular initial conditions. Besides, the IMEX time integrator allows to overcome the tiny time-step induced by the diffusive term in the explicit schemes, also providing very accurate and non-oscillatory approximations of the Greeks. Finally, in order to assess all the aforementioned good properties of the developed numerical schemes, we compute extremely accurate semi-analytic solutions using multi-dimensional Fourier cosine expansions. A novel technique to truncate the Fourier series for basket options is presented and it is efficiently implemented using multi-GPUs.

Date: 2024-10
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2410.02925 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2410.02925

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().