  We investigate exponential stock models driven by tempered stable processes,
which constitute a rich family of purely discontinuous L\'{e}vy processes. With
a view of option pricing, we provide a systematic analysis of the existence of
equivalent martingale measures, under which the model remains analytically
tractable. This includes the existence of Esscher martingale measures and
martingale measures having minimal distance to the physical probability
measure. Moreover, we provide pricing formulae for European call options and
perform a case study.
