1 Department of Business Studies, Aarhus School of Business, Aarhus BSS, Aarhus University2 Finance Research Group, Aarhus School of Business, Aarhus BSS, Aarhus University3 Department of Economics and Business Economics, Aarhus BSS, Aarhus University4 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
In reduced form default models, the instantaneous default intensity is classically the modeling object. Survival probabilities are then given by the Laplace transform of the cumulative hazard defined as the integrated intensity process. Instead, recent literature has shown a tendency towards specifying the cumulative hazard process directly. Within this framework we present a new model class where cumulative hazards are described by self-similar additive processes, also known as Sato processes. Furthermore we also analyze specifications obtained via a simple deterministic time-change of a homogeneous Levy process. While the processes in these two classes share the same average behavior over time, the associated intensities exhibit very different properties. Concrete specifications are calibrated to data on the single names included in the iTraxx Europe index. The performances are compared with those of a recently proposed class of intensity models based on Ornstein-Uhlenbeck type processes. It is shown how the time-inhomogeneous Levy models achieve comparable calibration errors with fever parameters, and with more stable parameter estimates over time. However, the calibration performances of the Sato processes and the time-change specifications are practically indistinguishable.
Credit default swap; reduced form model; Sato process; time-changed Lévy process; cumulative hazard