Hedging Exotic Options in Stochastic Volatility and Jump Diffusion Models

Fundamental progress has been made in developing more realistic option pricing models. While the hedging performance of these models has been investigated for plain vanilla options, it is still unknown how well these generalizations improve the hedging of exotic options. Using different barrier options on the DAX, we examine a stochastic volatility, a jump diffusion and a mixed model. We consider delta hedging, vega hedging and delta hedging with minimum variance in the Heston, the Bates and the Merton model. Thus, this work deals with the question of model selection that is nowadays of great importance because of the growing number of models and exotic products.