Before revision:  Laplace transform based approach is the clear separation of two ingredients, namely the payoff function and the underlying process . The latter can be the driving process itself, but also the supremum or infimum or another process derived from it. For L\'evy processes the analytically extended characteristic functions of the supremum and the infimum process are derived .
After revision:  Laplace transform based approach is the clear separation of two ingredients, namely the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models .