THE TIME-DEPENDENT FX-SABR MODEL: EFFICIENT CALIBRATION BASED ON EFFECTIVE PARAMETERS

Anthonie W. van der Stoep (), Lech Grzelak and Cornelis Oosterlee
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Anthonie W. van der Stoep: Pricing Model Validation, Rabobank, Graadt van Roggenweg 400, 3531 AH, Utrecht, The Netherlands;

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 06, 1-38

Abstract: We present a framework for efficient calibration of the time-dependent SABR model (Fernández et al. (2013) Mathematics and Computers in Simulation 94, 55–75; Hagan et al. (2002) Wilmott Magazine 84–108; Osajima (2007) Available at SSRN 965265.) in an foreign exchange (FX) context. In a similar fashion as in (Piterbarg (2005) Risk 18 (5), 71–75) 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 (Derman & Kani (1998) International Journal of Theoretical and Applied Finance 1 (1), 61–110; Dupire (1994) Risk 7 (1), 18–20). We also discuss 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 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024915500429

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