Time-changed CIR default intensities with two-sided mean-reverting jumps

The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process (X,D) of a diffusion state variable X driving default intensity and a default indicator process D and time change it with a Lévy subordinator T. We characterize the time-changed process (X.t,D.t)=(X(Tt),D(Tt)) as a Markovian.Itô semimartingale and show from the Doob.Meyer decomposition of D. that the default time in the time-changed model has a jump-diffusion or a pure jump intensity. When X is a CIR diffusion with mean-reverting drift, the default intensity of the subordinate model (SubCIR) is a jump-diffusion or a pure jump process with mean-reverting jumps in both directions that stays nonnegative. The SubCIR default intensity model is analytically tractable by means of explicitly computed eigenfunction expansions of relevant semigroups, yielding closed-form pricing of credit-sensitive securities.