Two-factor capital structure models for equity and credit

TL;DR

This paper introduces two-factor structural models that unify equity and credit derivatives, allowing for flexible dependence between markets and providing efficient pricing formulas for complex financial products.

Contribution

The paper develops a novel two-factor framework extending classical structural models to jointly model equity and credit, enabling more realistic dependence and efficient computation.

Findings

Models can reproduce features of variance gamma and structural credit risk.

Efficient pricing formulas for derivatives using two-dimensional FFT.

Enhanced dependence modeling between equity and credit markets.

Abstract

We extend the now classic structural credit modeling approach of Black and Cox to a class of "two-factor" models that unify equity securities such as options written on the stock price, and credit products like bonds and credit default swaps. In our approach, the two sides of the stylized balance sheet of a firm, namely the asset value and debt value, are assumed to follow a two dimensional Markov process. Amongst models of this type we find examples that lead to derivative pricing formulas that are capable of reproducing the main features of well known equity models such as the variance gamma model, and at the same time reproducing the stylized facts about default stemming from structural models of credit risk. Moreover, in contrast to one-factor structural models, these models allow for much more flexible dependence between equity and credit markets. Two main technical obstacles to efficient implementation of these pricing formulas are overcome in our paper. The first obstacle stems from the barrier condition implied by the non-default of the firm, and is overcome by the idea of time-changing Brownian motion in a way that preserves the reflection principle for Brownian motion. The second obstacle is the difficulty of computing spread options: this is overcome by using results in recent papers that make efficient use of the two dimensional Fast Fourier Transform.