Option Pricing using Lévy Processes

In this Master’s thesis we price exotic options using Monte Carlo simulations. The asset price process is modeled as an exponential Lévy process. First we use Lévy processes to fit the log-returns of S&P 500 historical data. By means of both graphical and quantitative tests we find that the NIG process and the Meixner perform better than the Brownian motion. Secondly, we calibrate NIG, Meixner and CGMY Lévy process models using S&P 500 index vanilla options. The calibration results show that non-Gaussian Lévy processes describes the market price better than Brownian motion. At last, we use the calibrated models to price exotic options