  We present a general framework for the estimation of corporate default based
on a firm's capital structure, when its assets are assumed to follow a pure
jump L\'evy processes; this setup provides a natural extension to usual default
metrics defined in diffusion (log-normal) models, and allows to capture extreme
market events such as sudden drops in asset prices, which are closely linked to
default occurrence. Within this framework, we introduce several pure jump
processes featuring negative jumps only and derive practical closed formulas
for equity prices, which enable us to use a moment-based algorithm to calibrate
the parameters from real market data and to estimate the associated default
metrics. A notable feature of these models is the redistribution of credit risk
towards shorter maturity: this constitutes an interesting improvement to
diffusion models, which are known to underestimate short term default
probabilities. We also provide extensions to a model featuring both positive
and negative jumps and discuss qualitative and quantitative features of the
results. For readers convenience, practical tools for model implementation and
GitHub links are also included.
