A tractable LIBOR model with default risk

TL;DR

This paper introduces an affine process-based LIBOR model that captures default risk, providing explicit formulas for credit derivatives and enabling practical counterparty risk assessment.

Contribution

It presents a novel, analytically tractable LIBOR model incorporating default risk using affine processes, with explicit formulas for credit derivatives.

Findings

Produces positive LIBOR rates and spreads

Derives explicit formulas for CDS spreads

Provides semi-analytical formulas for other credit derivatives

Abstract

We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are analytically tractable under defaultable forward measures. This leads to explicit formulas for CDS spreads, while semi-analytical formulas are derived for other credit derivatives. Finally, we give an application to counterparty risk.