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

by Luciano Campi of the Université Paris Dauphine,
Simon Polbennikov of Tilburg University, and
Alessandro Sbuelz of the University of Verona

November 2005

Abstract: Unlike in structural and reduced-form models, we use equity as a liquid and observable primitive to analytically value corporate bonds and credit default swaps. Restrictive assumptions on the firm's capital structure are avoided. Default is parsimoniously represented by equity value hitting the zero barrier. Default can be either predictable, according to a CEV process that yields a positive probability of diffusive default and enables the leverage effect, or unpredictable, according to a Poisson-process jump that implies non-zero credit spreads for short maturities. Easy cross-asset hedging ensues. By means of a carefully specified pricing kernel, we also empower analytical credit-risk management under possibly systematic jump-to-default risk.

JEL Classification: G12, G33.

Keywords: Equity, Corporate Bonds, Credit Default Swaps, Constant-Elasticity-of-Variance (CEV) Diffusion, Jump to Default.

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