This thesis deals with the calibration of stochastic volatility models. We analyze the Heston model as well as a jump-extension, the Bates model. The main goal is to provide a guideline along the way of model implementation and usage, as well as to analyze the differences, advantages and disadvantages of the two models. After deducting the pricing formulas of both models, we approach the problem of model calibration. Here we apply the Fast Fourier Transformation in order to accelerate the calibration procedure. We calibrate the models to market prices and analyze the behaviour of the model calibrations. Therefore, we choose different sets of weights and modify the models? restrictions and parameters. Afterwards, we implement Monte-Carlo pricing methods including a variance reduction technique via control variates in order to price exotic options. Thereafter, we manually shift certain parts of the volatility surface and test the models? flexibility of capturing these changes and analyze the evolution of the calibrated parameters caused by the shifts. Last but not least, we calibrate the Heston and the Bates model onto a whole time series of option prices to analyze the stability of the parameters over time.     «

This thesis deals with the calibration of stochastic volatility models. We analyze the Heston model as well as a jump-extension, the Bates model. The main goal is to provide a guideline along the way of model implementation and usage, as well as to analyze the differences, advantages and disadvantages of the two models. After deducting the pricing formulas of both models, we approach the problem of model calibration. Here we apply the Fast Fourier Transformation in order to accelerate the calibr...     »