A Structural Approach to Default Modelling with Pure Jump Processes

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