The Time-Dependent FX-SABR Model: Efficient Calibration Based on Effective Parameters

30 Pages Posted: 4 Oct 2014 Last revised: 28 Sep 2015

See all articles by Anthonie van der Stoep

Anthonie van der Stoep

Rabobank

Lech A. Grzelak

Delft University of Technology

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: May 25, 2015

Abstract

We present a framework for efficient calibration of the time-dependent SABR model in an FX context. In a similar fashion as in Piterbarg (2005) we derive effective parameters, which yield an accurate and efficient calibration. On top of the calibrated FX-SABR model we add a non-parametric local volatility component, which naturally compensates for possible calibration errors. By means of Monte Carlo pricing experiments we show that the time-dependent FX-SABR model enables an accurate and consistent pricing of barrier options and outperforms the constant-parameter SABR model and the traditional Local Volatility model. We also consider the role of the local volatility component in pricing barrier options.

Keywords: Time-Dependent SABR, FX, Calibration, Effective Parameters, Local Volatility, Monte Carlo, Path-Dependent

JEL Classification: C63, G12, G13

Suggested Citation

van der Stoep, Anthonie and Grzelak, Lech Aleksander and Oosterlee, Cornelis W., The Time-Dependent FX-SABR Model: Efficient Calibration Based on Effective Parameters (May 25, 2015). International Journal of Theoretical and Applied Finance, Vol. 18, No. 6 (2015). Available at SSRN: https://ssrn.com/abstract=2503891 or http://dx.doi.org/10.2139/ssrn.2503891

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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