Systematic Equity-based Credit Risk: A CEV model with jump to default

by Luciano Campi of Université Paris Dauphine,
Simon Polbennikov of Lehman Brothers International, Europe, and
Alessandro Sbuelz of University of Verona

August 2007

Abstract: We use equity as the traded primitive for a detailed analysis of systematic default risk. Default is parsimoniously represented by equity value hitting the zero barrier so that, unlike in reduced-form models, the explicit linkage to the firm's capital structure is preserved, but, unlike in structural models, restrictive assumptions on the structure are avoided. Default risk is either jump-like or diffusive. The equity price can jump to default. In line with recent empirical evidence on the jump-to-default risk price, we highlight how reasonable choices of the pricing kernel can imply remarkable differences in the equity-price-dependent status between the objective default intensity and the risk-neutral intensity. As equity returns experience negative diffusive shocks, their CEV-type local variance increases and boosts the objective and risk-neutral probabilities of diffusive default. A parsimonious version of our general model simultaneously enables analytical credit-risk management and analytical pricing of credit-sensitive instruments. Easy cross-asset hedging ensues.

JEL Classification: G12, G33.

Keywords: Market price of credit risk, Constant-elasticity-of-variance (CEV) diffusive risk, Jump-to-default risk, Equity, Corporate bonds, Credit default swaps.

Published in: Journal of Economic Dynamics and Control, Vol. 33, No. 1, (January 2009), pp. 93-108.

Previously titled: Assessing Credit with Equity: A CEV Model with Jump to Default

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