Volatility smile modelling approaches

The Master's thesis is dedicated to the methods of modelling a volatility smile. The volatility smile is a common pattern of implied volatilities of a group of options plotted against the strikes of those option contracts. The curve arises from the inaccuracy of the Black-Scholes option pricing formula. The purpose of this thesis is to list and compare different approaches as well as to apply some of the models on real market data in order to verify theoretical findings. The first chapter of the thesis is devoted to the basics of option contracts as well as to the history of the volatility smile. The second part provides detailed information about the most well-known option pricing models that can be used for modelling purposes. The third part is dedicated to the calibration and comparison of two modelling approaches - the Heston model and the Stochastic-Volatility with Jump-Diffusion model.