Consider asset price dynamics models driven
by L\'evy processes, in particular, gamma processes, stable
processes, tempered stable processes, and time-changed Brownian motions.
In this talk, we shall present the sensitivity formulas,
via an application of the Malliavin calculus for jump processes
by making use of the Girsanov transform. Our asset price models
can be of a pure-jump type, and of infinite activity type.
Numerical results illustrate the effectiveness of our derived
formulas in Monte Carlo simulations relative to the finite
difference methods. This talk is based upon joint works with
R. Kawai (University of Leicester, UK).