Second Order Finite Volume IMEX Runge-Kutta Schemes for Two Dimensional Parabolic PDEs in Finance
Title
Second Order Finite Volume IMEX Runge-Kutta Schemes for Two Dimensional Parabolic PDEs in FinanceDate
2024-06-06Citation
López-Salas, J.G., Suárez-Taboada, M., Castro, M.J., Ferreiro-Ferreiro, A.M., García-Rodríguez, J.A. (2024). Second Order Finite Volume IMEX Runge-Kutta Schemes for Two Dimensional Parabolic PDEs in Finance. 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_13
Abstract
[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.
Keywords
Finite volume
IMEX
Mathematical finance
IMEX
Mathematical finance
Description
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG ©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_13 The conference was held in Málaga, Spain, June 20-24, 2022
Editor version
ISSN
2199-3041
2199-305X
2199-305X
ISBN
978-3-031-55263-2 978-3-031-55266-3 978-3-031-55264-9
