On an Efficient Multiple Time-Step Monte Carlo Simulation of the SABR Model

Quantitative Finance 17(10): 1549-1565, 2017

28 Pages Posted: 17 Apr 2016 Last revised: 28 Oct 2018

See all articles by Alvaro Leitao Rodriguez

Alvaro Leitao Rodriguez

University of Coruña - Department of Mathematics - M2NICA

Lech A. Grzelak

Delft University of Technology

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: April 12, 2016

Abstract

In this paper, we will 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 an accompanying paper, for pricing European options in the context of the model calibration. A highly efficient method results, with many highly 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 options and for exotic options.

Keywords: SABR model; Exact simulation; Monte Carlo methods; Copulas; Stochastic collocation; Fourier techniques; Exotic options

JEL Classification: C15; C63

Suggested Citation

Leitao Rodriguez, Alvaro and Grzelak, Lech Aleksander and Oosterlee, Cornelis W., On an Efficient Multiple Time-Step Monte Carlo Simulation of the SABR Model (April 12, 2016). Quantitative Finance 17(10): 1549-1565, 2017. Available at SSRN: https://ssrn.com/abstract=2764908 or http://dx.doi.org/10.2139/ssrn.2764908

Alvaro Leitao Rodriguez (Contact Author)

University of Coruña - Department of Mathematics - M2NICA ( email )

Campus Elvina s/n
A Coruna, 15071
Spain

Lech Aleksander Grzelak

Delft University of Technology ( email )

Netherlands
00310655731315 (Phone)

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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