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

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.