AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE Models
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AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE ModelsDate
2021-01Citation
López-Salas, José G., Soledad Pérez-Rodríguez, and Carlos Vázquez. "AMFR-W numerical methods for solving high-dimensional SABR/LIBOR PDE models." SIAM Journal on Scientific Computing 43, no. 1 (2021): B30-B54. https://doi.org/10.1137/20M1348595
Abstract
[Abstract]: In this work, we mainly develop a new numerical methodology to solve a PDE model recently proposed in the literature for pricing interest rate derivatives. More precisely, we use high-order-in-time AMFR-W-methods, which belong to a class of W-methods based on approximate matrix factorization (AMF) and are especially suitable in the presence of mixed spatial derivatives. High-order convergence in time allows larger time steps, which, combined with the splitting of the involved operators, highly reduces the computational time for a given accuracy. Moreover, the consideration of a large number of underlying forward rates makes the PDE problem high dimensional in space, so the use of AMFR-W-methods with a sparse grid combination technique represents another innovative aspect, making AMFR-W more efficient than with full grids and opening the possibility of parallelization. Also, the consideration of new homogeneous Neumann boundary conditions provides another original feature to avoid the difficulties associated to the presence of boundary layers when using Dirichlet ones, especially in advection-dominated regimes. These Neumann boundary conditions motivate the introduction of a modified combination technique to overcome a decrease in the accuracy of the standard combination technique.
Keywords
SABR-LIBOR market models
high-dimensional PDEs
AMFR-W-methods
Finite differences
Sparse grid combination technique
high-dimensional PDEs
AMFR-W-methods
Finite differences
Sparse grid combination technique
Description
©2021 Society for Industrial and Applied Mathematics (SIAM). This version of the article has been accepted for publication, after peer review, 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/10.1137/20M1348595
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Atribución 3.0 España
ISSN
1064-8275
1095-7197
1095-7197