Default risk modeling beyond the first-passage approximation: Position-dependent killing

TL;DR

This paper develops a position-dependent diffusion model with variable killing rates to better understand default risk, deriving closed-form solutions and validating them with historical corporate default data.

Contribution

It introduces a novel perturbation approach for modeling default risk beyond the first-passage approximation, accounting for position-dependent effects.

Findings

Model accurately captures the rarity of defaults in investment-grade categories.

Closed-form expressions for default probability and hazard rate are derived.

Model aligns well with historical corporate default data.

Abstract

Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to diverse models of bankruptcy. One "stylized fact" is fundamental for our consideration: empirically default is a rather rare event, especially in the investment grade categories of credit ratings. Hence, the action of killing may be considered as a small parameter. In a number of special cases we derive closed-form expressions for the entire term structure of the cumulative probability of default, its hazard rate and intensity. Comparison with historical data on global corporate defaults confirms applicability of the model-independent perturbation method for companies in the investment grade categories of credit ratings and allows for