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For a spectrally negative L\'evy process $X$, we study the followingdistribution: $$ \mathbb{E}_x \left[ \mathrm{e}^{- q \int_0^t\mathbf{1}_{(a,b)} (X_s) \mathrm{d}s } ; X_t \in \mathrm{d}y \right], $$ where$-\infty \leq a < b < \infty$, and where $q,t>0$ and $x \in \mathbb{R}$. Moreprecisely, we identify the Laplace transform with respect to $t$ of thismeasure in terms of the scale functions of the underlying process. Our resultsare then used to price step options and the particular case of an exponentialspectrally negative L\'evy jump-diffusion model is discussed.

Joint distribution of a spectrally negative L\'evy process and its occupation time, with step option pricing in view