  The present article deals with intra-horizon risk in models with jumps. Our
general understanding of intra-horizon risk is along the lines of the approach
taken in Boudoukh, Richardson, Stanton and Whitelaw (2004), Rossello (2008),
Bhattacharyya, Misra and Kodase (2009), Bakshi and Panayotov (2010), and
Leippold and Vasiljevi\'c (2019). In particular, we believe that quantifying
market risk by strictly relying on point-in-time measures cannot be deemed a
satisfactory approach in general. Instead, we argue that complementing this
approach by studying measures of risk that capture the magnitude of losses
potentially incurred at any time of a trading horizon is necessary when dealing
with (m)any financial position(s). To address this issue, we propose an
intra-horizon analogue of the expected shortfall for general profit and loss
processes and discuss its key properties. Our intra-horizon expected shortfall
is well-defined for (m)any popular class(es) of L\'evy processes encountered
when modeling market dynamics and constitutes a coherent measure of risk, as
introduced in Cheridito, Delbaen and Kupper (2004). On the computational side,
we provide a simple method to derive the intra-horizon risk inherent to popular
L\'evy dynamics. Our general technique relies on results for
maturity-randomized first-passage probabilities and allows for a derivation of
diffusion and single jump risk contributions. These theoretical results are
complemented with an empirical analysis, where popular L\'evy dynamics are
calibrated to S&P 500 index data and an analysis of the resulting intra-horizon
risk is presented.
