Ambiguity in defaultable term structure models

TL;DR

This paper develops a framework for understanding no-arbitrage conditions in credit risk markets with ambiguous default intensities, using Girsanov theorem and $G$-expectation to derive bounds on bond prices.

Contribution

It introduces a novel approach to model ambiguity in default intensities within a no-arbitrage framework, connecting credit risk with drift uncertainty models.

Findings

Derived the set of equivalent martingale measures under ambiguity.

Established the interval of no-arbitrage bond prices in a Markovian setting.

Linked credit risk ambiguity to $G$-expectation framework.

Abstract

We introduce the concept of no-arbitrage in a credit risk market under ambiguity considering an intensity-based framework. We assume the default intensity is not exactly known but lies between an upper and lower bound. By means of the Girsanov theorem, we start from the reference measure where the intensity is equal to $1$ and construct the set of equivalent martingale measures. From this viewpoint, the credit risky case turns out to be similar to the case of drift uncertainty in the $G$-expectation framework. Finally, we derive the interval of no-arbitrage prices for general bond prices in a Markovian setting.