Credit Bubbles in Arbitrage Markets: The Geometric Arbitrage Approach to Credit Risk

TL;DR

This paper applies Geometric Arbitrage Theory to credit markets to derive explicit formulas for arbitrage conditions, default intensities, and credit bubbles, providing a geometric framework that avoids stochastic differential geometry.

Contribution

It introduces a geometric approach to credit risk modeling that yields explicit formulas for arbitrage conditions and credit bubbles without relying on stochastic differential geometry.

Findings

Explicit formulas for no-arbitrage conditions in credit markets.

Characterization of credit bubbles in arbitrage-minimized market dynamics.

Derivation of dynamics involving default intensities and loss given defaults.

Abstract

We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and loss given defaults characterizing the no-free-lunch-with-vanishing-risk condition for corporate bonds, as well as the generic dynamics for credit market allowing for arbitrage possibilities. Moreover, arbitrage credit bubbles for both base credit assets and credit derivatives are explicitly computed for the market dynamics minimizing the arbitrage.