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Sparse Grid Combination Technique for Hagan SABR/LIBOR Market Model
dc.contributor.author | López Salas, José Germán | |
dc.contributor.author | Vázquez, Carlos | |
dc.date.accessioned | 2024-07-18T12:33:41Z | |
dc.date.available | 2024-07-18T12:33:41Z | |
dc.date.issued | 2017-09-20 | |
dc.identifier.citation | López-Salas, J.G., Cendón, C.V. (2017). Sparse Grid Combination Technique for Hagan SABR/LIBOR Market Model. In: Ehrhardt, M., Günther, M., ter Maten, E. (eds) Novel Methods in Computational Finance. Mathematics in Industry, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-61282-9_27 | es_ES |
dc.identifier.isbn | 978-3-319-61281-2 | |
dc.identifier.isbn | 978-3-319-61282-9 | |
dc.identifier.issn | 2198-3283 | |
dc.identifier.issn | 1612-3956 | |
dc.identifier.uri | http://hdl.handle.net/2183/38150 | |
dc.description | ©2017 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/10.1007/978-3-319-61282-9_27 | es_ES |
dc.description.abstract | [Abstract]: SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, the pricing of derivatives with SABR/LIBOR market models (SABR/LMMs) is mainly carried out with Monte Carlo simulation. However, this approach could involve excessively long computational times. In the present chapter we propose an alternative pricing based on partial differential equations (PDEs). Thus, we pose the PDE formulation associated to the SABR/LMM proposed by Hagan and Lesniewski (LIBOR market model with SABR style stochastic volatility. Working paper, available at http://lesniewski.us/papers/working/SABRLMM.pdf (2008)). As this PDE is high dimensional in space, traditional full grid methods (like standard finite differences or finite elements) are not able to price derivatives over more than one or two underlying interest rates and their corresponding stochastic volatilities. In order to overcome this curse of dimensionality, a sparse grid combination technique is proposed. So as to assess on the performance of the method a comparison with Monte Carlo is presented. | es_ES |
dc.description.sponsorship | Partially financed by Spanish Grant MTM2013-47800-C2-1-P and by Xunta de Galicia (Grant CN2014/044). First author has also been founded by a FPU Spanish Grant | es_ES |
dc.description.sponsorship | Xunta de Galicia; CN2014/044 | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Springer | es_ES |
dc.relation | Info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2013-47800-C2-1-P/ES/MODELADO MATEMATICO, ANALISIS Y SIMULACION NUMERICA DE PROBLEMAS EN FINANZAS Y SEGUROS, PROCESOS INDUSTRIALES, BIOTECNOLOGIA Y MEDIOAMBIENTE | es_ES |
dc.relation.uri | https://doi.org/10.1007/978-3-319-61282-9_27 | es_ES |
dc.subject | Stochastic volatility models | es_ES |
dc.subject | SABR/LIBOR market models | es_ES |
dc.subject | Sparse grids | es_ES |
dc.subject | Combination technique | es_ES |
dc.title | Sparse Grid Combination Technique for Hagan SABR/LIBOR Market Model | es_ES |
dc.type | info:eu-repo/semantics/bookPart | es_ES |
dc.rights.access | info:eu-repo/semantics/openAccess | es_ES |
UDC.journalTitle | Mathematics in Industry | es_ES |
UDC.volume | 25 | es_ES |
UDC.startPage | 477 | es_ES |
UDC.endPage | 500 | es_ES |