SABR Model Extensions for Negative Rates

Abstract: In this report, we present extensions of the SABR model to negative rates applied to the swaption market. We start by briefly presenting the classical SABR model. Then we study the Shifted, Free Boundary and Mixture SABR Models. Numerical experiments are performed on these models to assess their performance, in particular we detail the calibration process for the Mixture SABR and apply it on market data.