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The Time-Dependent Fx-Sabr Model: Efficient Calibration Based On Effective Parameters

Author

Listed:
  • ANTHONIE W. VAN DER STOEP

    (Pricing Model Validation, Rabobank, Graadt van Roggenweg 400, 3531 AH, Utrecht, The Netherlands;
    CWI — National Research Institute for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands)

  • LECH A. GRZELAK

    (Pricing Model Validation, Rabobank, Graadt van Roggenweg 400, 3531 AH, Utrecht, The Netherlands;
    Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands)

  • CORNELIS W. OOSTERLEE

    (CWI — National Research Institute for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands;
    Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands)

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.

Suggested Citation

  • Anthonie W. Van Der Stoep & Lech A. Grzelak & Cornelis W. Oosterlee, 2015. "The Time-Dependent Fx-Sabr Model: Efficient Calibration Based On Effective Parameters," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-38.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:06:n:s0219024915500429
    DOI: 10.1142/S0219024915500429
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    Cited by:

    1. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.

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