The Impossible Trio in CDO Modeling

TL;DR

This paper demonstrates that stochastic recovery models in CDOs inherently produce conflicting behaviors in risk measures, and introduces a regularization method to mitigate negative spread risk while maintaining default continuity.

Contribution

It reveals the fundamental trade-offs in stochastic recovery modeling and proposes a novel regularization approach to address these issues.

Findings

Stochastic recovery causes counter-intuitive risk measure behaviors.

Continuity on default and positive spread risk cannot be achieved simultaneously.

Recovery variance regularization helps control negative spread risk.

Abstract

We show that stochastic recovery always leads to counter-intuitive behaviors in the risk measures of a CDO tranche - namely, continuity on default and positive credit spread risk cannot be ensured simultaneously. We then propose a simple recovery variance regularization method to control the magnitude of negative credit spread risk while preserving the continuity on default.