Sparse Grid Combination Technique for Hagan SABR/LIBOR Market Model
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Sparse Grid Combination Technique for Hagan SABR/LIBOR Market ModelDate
2017-09-20Citation
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
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.
Keywords
Stochastic volatility models
SABR/LIBOR market models
Sparse grids
Combination technique
SABR/LIBOR market models
Sparse grids
Combination technique
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
Editor version
ISSN
2198-3283
1612-3956
1612-3956
ISBN
978-3-319-61281-2 978-3-319-61282-9