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In mathematical Finance calculating the Greeks by Malliavin weights hasproved to be a numerically satisfactory procedure for finite-dimensionalIt\^{o}-diffusions. The existence of Malliavin weights relies on absolutecontinuity of laws of the projected diffusion process and a sufficientlyregular density. In this article we first prove results on absolute continuityfor laws of projected jump-diffusion processes in finite and infinitedimensions, and a general result on the existence of Malliavin weights infinite dimension. In both cases we assume H\"ormander conditions and hypotheseson the invertibility of the so-called linkage operators. The purpose of thisarticle is to show that for the construction of numerical procedures for thecalculation of the Greeks in fairly general jump-diffusion cases one canproceed as in a pure diffusion case. We also show how the given results applyto infinite dimensional questions in mathematical Finance. There we start fromthe Vasi\v{c}ek model, and add -- by pertaining no arbitrage -- a jumpdiffusion component. We prove that we can obtain in this case an interest ratemodel, where the law of any projection is absolutely continuous with respect toLebesgue measure on $\mathbb{R}^M $.

Absolutely Continuous Laws of Jump-Diffusions in Finite and Infinite Dimensions with Applications to Mathematical Finance