The SABR model in financial practice

Abstract

The Black-Scholes model fails to reproduce some empirical properties of volatility, from real market data, which means that the model may not be adequate to price certain options. Hence, the financial industry and academia focused on developing alternative models and methods for pricing. One of these models is the SABR model, a stochastic volatility model commonly used in nowadays financial industry. In this project, we aim to analyze and discuss the SABR model from both the theoretical and the practical point of view by motivating the usage of this model and showing how it can be applied in different aspects of the financial practice such as calibration, simulation and numerical methods to obtain implied volatilities. Throughout this analysis and discussion, we also aim to give some insights regarding what practitioners do, to give some sense of the applicability of the model and the methods in the real world.