Swaption pricing with SABR model

Abstract

The purpose of this Master’s thesis is to present the SABR and shifted SABR models and perform a calibration procedure on the Euribor and Libor swaptions’ volatility cube. The first chapter focuses on the mathematical preliminaries for interest rate derivatives and money market. The second chapter tackles the classical option pricing models, in particular Black-76 model. The third chapter introduces SABR model and Hagan’s approximation formulas, as well as the shifted SABR and the effects of SABR parameters on the volatility smiles and skews. Finally, the last chapter shows the detailed procedure of calibration of the Euribor and Libor volatility cubes, validation of the fit and some market data engineering examples referencing to the python code in the appendix.