PDE formulation of some SABR/LIBOR market models and its numerical solution with a sparse grid combination technique
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PDE formulation of some SABR/LIBOR market models and its numerical solution with a sparse grid combination techniqueData
2018-03-01Cita bibliográfica
J. G. López-Salas y C. Vázquez, «PDE formulation of some SABR/LIBOR market models and its numerical solution with a sparse grid combination technique», Computers & Mathematics with Applications, vol. 75, n.o 5, pp. 1616-1634, mar. 2018, doi: 10.1016/j.camwa.2017.11.024.
Resumo
[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. For first time in the literature, in the present paper we propose an alternative pricing based on partial differential equations (PDEs). Thus, we pose original PDE formulations associated to the SABR/LMMs proposed by Hagan and Lesniewsk (2008), Mercurio and Morini (2009) and Rebonato and White (2008). Moreover, as the PDEs associated to these SABR/LMMs are high dimensional in space, traditional full grid methods (like standard finite differences or finite elements) are not able to price derivatives over more than three or four underlying interest rates. In order to overcome this curse of dimensionality, a sparse grid combination technique is proposed. A comparison between Monte Carlo simulation results and the ones obtained with the sparse grid technique illustrates the performance of the method.
Palabras chave
Stochastic volatility models
SABR/LIBOR market models
High dimensional PDEs
Sparse grids
Combination technique
SABR/LIBOR market models
High dimensional PDEs
Sparse grids
Combination technique
Descrición
© 2018 Elsevier. This manuscript version is made available under the CCBY-
NC-ND 4.0 license https://creativecommons.org/licenses/by-ncnd/
4.0/. This version of the article has been accepted for publication in
Computers & Mathematics with Applications. The Version of Record is
available online at https://doi.org/10.1016/j.camwa.2017.11.024.
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Atribución-NoComercial-SinDerivadas 3.0 España
ISSN
1873-7668
0898-1221
0898-1221