The time-dependent FX-SABR model: Efficient calibration based on effective parameters

We present a framework for efficient calibration of the time-dependent SABR model (Fern´andez 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.