A structural approach to default modelling with pure jump processes

TL;DR

This paper introduces a new framework for modeling corporate default using pure jump processes, capturing extreme market events and improving short-term default probability estimates over traditional diffusion models.

Contribution

It develops a general pure jump process framework for default modeling, providing closed-form equity pricing formulas and calibration methods from market data.

Findings

Models better capture sudden asset drops and short-term default risks.

Closed-form formulas enable practical calibration from real market data.

Extensions include models with both positive and negative jumps.

Abstract

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.