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 Levy subordinator T. We characterize the time-changed process (X-t(phi), D-t(phi)) = (X (T-t), D (T-t)) as a Markovian Ito semimartingale and show from the Doob-Meyer decomposition of D-phi 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.