Dependence of defaults and recoveries in structural credit risk models

TL;DR

This paper explores the intrinsic connection between default probabilities and recovery rates in structural credit risk models, deriving a functional relation that improves the modeling of tail losses.

Contribution

It introduces a functional relation between recovery rates and default probabilities based on the Merton model, applicable to various stochastic processes, enhancing reduced-form models.

Findings

The relation depends on a single parameter.

The relation holds for jump-diffusion and GARCH processes.

Incorporating this improves tail loss modeling.

Abstract

The current research on credit risk is primarily focused on modeling default probabilities. Recovery rates are often treated as an afterthought; they are modeled independently, in many cases they are even assumed constant. This is despite of their pronounced effect on the tail of the loss distribution. Here, we take a step back, historically, and start again from the Merton model, where defaults and recoveries are both determined by an underlying process. Hence, they are intrinsically connected. For the diffusion process, we can derive the functional relation between expected recovery rate and default probability. This relation depends on a single parameter only. In Monte Carlo simulations we find that the same functional dependence also holds for jump-diffusion and GARCH processes. We discuss how to incorporate this structural recovery rate into reduced form models, in order to restore essential structural information which is usually neglected in the reduced-form approach.