Speedup of Calibration and Pricing with SABR Models: From Equities to Interest Rates Derivatives
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Speedup of Calibration and Pricing with SABR Models: From Equities to Interest Rates DerivativesAutor(es)
Data
2015Cita bibliográfica
Ferreiro, A.M., García-Rodríguez, J.A., López-Salas, J.G., Vázquez, C. (2015). Speedup of Calibration and Pricing with SABR Models: From Equities to Interest Rates Derivatives. In: Londoño, J., Garrido, J., Hernández-Hernández, D. (eds) Actuarial Sciences and Quantitative Finance. Springer Proceedings in Mathematics & Statistics, vol 135. Springer, Cham. https://doi.org/10.1007/978-3-319-18239-1_4
Resumo
[Abstract]: In the more classical models for equities and interest rates evolution, constant volatility is usually assumed. However, in practice the volatilities are not constant in financial markets and different models allowing a varying local or stochastic volatility also appear in the literature. Particularly, here we consider the SABR model that has been first introduced in a paper by Hagan and coworkers, where an asymptotic closed-form formula for the implied volatility of European plain-vanilla options with short maturities is proposed. More recently, different works (Mercurio and Morini, Modeling Interest Rates: Advances in Derivatives Pricing, Risk Books 2009; Hagan and Lesniewski, LIBOR market model with SABR style stochastic volatility. Working Paper. http://lesniewski.us/papers/working/SABRLMM.pdf, 2008; Rebonato, A time-homogeneous SABR-consistent extension of the LMM. Risk, 2008) have extended the use of SABR model in the context of LIBOR market models for the evolution of forward rates (SABR-LMM). One drawback of these models in practice comes from the increase of computational cost, mainly due to the growth of model parameters to be calibrated. Additionally, sometimes either it is not always possible to compute an analytical approximation for the implied volatility or its expression results to be very complex, so that numerical methods (for example, Monte Carlo in the calibration process) have to be used. In this work we mainly review some recently proposed global optimization techniques based on Simulated Annealing (SA) algorithms and its implementation on Graphics Processing Units (GPUs) in order to highly speed up the calibration and pricing of different kinds of options and interest rate derivatives. Finally, we present some examples corresponding to real market data.
Palabras chave
SABR volatility models
SABR/LIBOR market models
Parallel simulated annealing
GPUs
SABR/LIBOR market models
Parallel simulated annealing
GPUs
Descrición
©2015 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/10.1007/978-3-319-18239-1_4 ICASQF2016 was held in Cartagena, Colombia, June 2016
Versión do editor
ISSN
2194-1017
2194-1009
2194-1009
ISBN
978-3-319-18238-4 978-3-319-18239-1