On a One Time-Step SABR Simulation Approach: Application to European Options

Applied Mathematics and Computation 293: 461-479, 2017

25 Pages Posted: 16 Apr 2016 Last revised: 27 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

Utrecht University - Faculty of Science

Date Written: February 10, 2016

Abstract

In this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the integrated variance (conditional on the SABR volatility process), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alternative to Hagan's analytic formula for short maturities that may be employed for model calibration purposes.

Keywords: Computational finance, Stochastic-local volatility models, SABR model, Copulas

Suggested Citation

Leitao Rodriguez, Alvaro and Grzelak, Lech Aleksander and Oosterlee, Cornelis W., On a One Time-Step SABR Simulation Approach: Application to European Options (February 10, 2016). Applied Mathematics and Computation 293: 461-479, 2017, Available at SSRN: https://ssrn.com/abstract=2731537 or http://dx.doi.org/10.2139/ssrn.2731537

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

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands

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