Credit Risk in Pure Jump Structural Models

Abstract

Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In particular, assuming a pure jump process. Moreover, when applied to market data diffusion-based structural models tend to produce too low spreads, even over longer horizons. In this paper we show that a jump process of the Variance-Gamma type for the asset value can also circumvent this practical shortcoming. We calibrate a terminal-default jump structural model to single-name data for the CDX NA IG and CDX NA HY components. We show that the VG model provides not only smaller errors, but also a better qualitative fit than other diffusive structural models. Indeed, it avoids both the spread underprediction of the classical Merton model and the excessive overpredictions of other well known diffusive models, as recently explored by Eom, Helwege, Huang (2004) or Demchuk and Gibson (2005).