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.
Null option (theme 11)
World Scientific
International Journal of Theoretical and Applied Finance
Scientific Computing

van der Stoep, A.W, Grzelak, L.A, & Oosterlee, C.W. (2015). The time-dependent FX-SABR model: Efficient calibration based on effective parameters. International Journal of Theoretical and Applied Finance, 18(6).