Abstract
In this work, we present a multiple time-step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho (SABR) model. The proposed method is an extension of the one time-step Monte Carlo method that we proposed in Leitao et al. (Appl. Math. Comput. 293: 461–479, 2017). We call it the mSABR method. A highly efficient method results, with many interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time-step Monte Carlo method is especially useful for long-term or for exotic options. This paper is a short version of an already published paper (Leitao et al. On an efficient multiple time-step Monte Carlo simulation of the SABR model. Quantitative Finance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Andersen, L.B.G.: Efficient simulation of the Heston stochastic volatility model. J. Comput. Finance 11, 1–22 (2008)
Chen, B., Oosterlee, C.W., van der Weide, H.: A low-bias simulation scheme for the SABR stochastic volatility model. Int. J. Theor. Appl. Finance 15, 1250016-1–1250016-37 (2012)
Fang, F., Oosterlee, C.W.: A novel pricing method for European options based on Fourier-cosine series expansions. SIAM J. Sci. Comput. 31, 826–848 (2008)
Grzelak, L.A., Witteveen, J.A.S., Suárez-Taboada, M., Oosterlee, C.W.: The stochastic collocation Monte Carlo sampler: highly efficient sampling from “expensive” distributions. Available at SSRN. https://ssrn.com/abstract=2529691 (2015)
Hagan, P.S., Kumar, D., Lesniewski, A.S., Woodward, D.E.: Managing smile risk. Wilmott Mag. January, 84–108 (2002)
Islah, O.: Solving SABR in exact form and unifying it with LIBOR market model. Available at SSRN. http://ssrn.com/abstract=1489428 (2009)
Leitao, A., Grzelak, L.A., Oosterlee, C.W.: On an efficient multiple time-step Monte Carlo simulation of the SABR model. Quantitative Finance. http://dx.doi.org/10.1080/14697688.2017.1301676
Leitao, A., Grzelak, L.A., Oosterlee, C.W.: On a one time-step Monte Carlo simulation approach of the SABR model: application to European options. Appl. Math. Comput. 293, 461–479 (2017)
Zhang, B., Oosterlee, C.W.: Efficient pricing of European-style Asian options under exponential Lévy processes based on Fourier cosine expansions. SIAM J. Financ. Math. 4, 399–426 (2013)
Acknowledgements
Supported by the EU in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE—Novel Methods in Computational Finance.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Leitao, Á., Grzelak, L.A., Oosterlee, C.W. (2017). Efficient Multiple Time-Step Simulation of the SABR Model. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-63082-3_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-63081-6
Online ISBN: 978-3-319-63082-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)