Introducing and testing the Carr model of default
The Merton model (1974) in is often considered the simplest structural model of default. Its famous modification developed by KMV is also widely used and well-understood by both practitioners and academics. However, being the underlying asset process driven by a diffusion process, the Merton model suffers from the well-known issue of vanishing of credit spreads for progressively shorter maturities. To overcome such shortfall, several modifications have been proposed in the literature; however, none of these, despite succeeding at better pricing spreads and explaining default dynamics, are able to retain the simplicity of the Merton model. In this paper, we propose a new structural model of default driven by additive process which is furthermore able to produce pricing formulas as simple as -- if not even simpler than -- those of the Merton model. We named such model the Carr model of default after Peter Carr, given his recent passing and the fact that the underlying asset distribution is the one introduced in Carr and Torricelli (2021) and Carr and Maglione (2022). We first provide pricing formulas for the firm's claims and credit spreads, and then discuss a general theory of change of measure for such processes in order to introduce a distance-to-default version of this newly-introduced model. Finally, we empirically test the Carr versus the Merton model and document a far better ability of the Carr model to both reproduce CDS spreads as well as explain their cross-sectional and time-series variations.
Area: CS44 - Algebraic option pricing and probability: in honor of Peter Carr (Umberto Cherubini and Sabrina Mulinacci)
Keywords: Credit risk, distance-to-default, Merton model, default probabilities, additive processes
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