Before revision:  Several illustrative examples of the new concept are given , among them a novel result on the Margrabe option to exchange one defaultable asset for another.
After revision:  The calculus is also intuitive as it allows the user to pretend all jumps are of compound Poisson type. The new calculus is very effective when it comes to computing drifts and expected values that possibly involve a change of measure. Such drift calculations yield, for example, partial integro-differential equations, Hamilton-Jacobi-Bellman equations, Feynman-Kac formulae, or exponential moments needed in numerous applications. We provide several illustrations of the new technique , among them a novel result on the Margrabe option to exchange one defaultable asset for another.