Efficient Multiple Time-Step Simulation of the SABR Model
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.
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.
- 2.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)Google Scholar
- 4.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)
- 5.Hagan, P.S., Kumar, D., Lesniewski, A.S., Woodward, D.E.: Managing smile risk. Wilmott Mag. January, 84–108 (2002)Google Scholar
- 6.Islah, O.: Solving SABR in exact form and unifying it with LIBOR market model. Available at SSRN. http://ssrn.com/abstract=1489428 (2009)
- 7.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