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AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE Models
dc.contributor.author | López Salas, José Germán | |
dc.contributor.author | Pérez-Rodríguez, Soledad | |
dc.contributor.author | Vázquez, Carlos | |
dc.date.accessioned | 2024-07-22T10:38:55Z | |
dc.date.available | 2024-07-22T10:38:55Z | |
dc.date.issued | 2021-01 | |
dc.identifier.citation | 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 | es_ES |
dc.identifier.issn | 1064-8275 | |
dc.identifier.issn | 1095-7197 | |
dc.identifier.uri | http://hdl.handle.net/2183/38185 | |
dc.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 | es_ES |
dc.description.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. | es_ES |
dc.description.sponsorship | This work was funded by the Spanish Grants MTM2016-76497-R, PID2019-108584- RB-I00 and MTM2016-77735-C3-3-P, as well as Xunta de Galicia grant ED431C2018/033, all includ- ing FEDER funding. First and third authors acknowledge the support received from the Centro de Investigacin de Galicia "CITIC", funded by Xunta de Galicia and the European Union (European Regional Development Fund- Galicia 2014-2020 Program), by grant ED431G 2019/01. | es_ES |
dc.description.sponsorship | Xunta de Galicia; ED431C2018/033 | es_ES |
dc.description.sponsorship | Xunta de Galicia; ED431G 2019/01 | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Society for Industrial and Applied Mathematics (SIAM) | es_ES |
dc.relation | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-76497-R/ES/METODOS MATEMATICOS Y SIMULACION NUMERICA PARA RETOS EN FINANZAS CUANTITATIVAS, MEDIOAMBIENTE, BIOTECNOLOGIA Y EFICIENCIA INDUSTRIAL | es_ES |
dc.relation | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108584RB-I00/ES/METODOS MATEMATICOS Y COMPUTACIONALES PARA NUEVOS RETOS EN FINANZAS CUANTITATIVAS, MEDIAMBIENTE, BIOTECNOLOGIA E INGENIERIA/ | es_ES |
dc.relation | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-77735-C3-3-P/ES/INTEGRADORES TEMPORALES EFICIENTES PARA PROBLEMAS DIFERENCIALES CON CARACTERÍSTICAS ESPECIALES. W-MÉTODOS Y TÉCNICAS DE SPLITTING PARA EDPS (ETSM_DPSC) | es_ES |
dc.relation.uri | https://doi.org/10.1137/20M1348595 | es_ES |
dc.rights | Atribución 3.0 España | es_ES |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject | SABR-LIBOR market models | es_ES |
dc.subject | high-dimensional PDEs | es_ES |
dc.subject | AMFR-W-methods | es_ES |
dc.subject | Finite differences | es_ES |
dc.subject | Sparse grid combination technique | es_ES |
dc.title | AMFR-W Numerical Methods for Solving High-Dimensional SABR/LIBOR PDE Models | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.access | info:eu-repo/semantics/openAccess | es_ES |
UDC.journalTitle | SIAM Journal on Scientific Computing | es_ES |
UDC.volume | 43 | es_ES |
UDC.issue | 1 | es_ES |
UDC.startPage | B30 | es_ES |
UDC.endPage | B54 | es_ES |
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