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

Rafael Mendoza-Arriaga, Vadim Linetsky

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

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 τ .We characterize the time-changed process (X φ t ,D φ t ) = (X(Tt ),D(Tt )) as a Markovian.Ito semimartingale and show from the Doob.Meyer decomposition of Dφ 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.

Original languageEnglish (US)
Pages (from-to)811-856
Number of pages46
JournalAnnals of Applied Probability
Volume24
Issue number2
DOIs
StatePublished - Apr 2014

Keywords

  • Bochner subordination
  • CIR process
  • Corporate bond
  • Credit derivative
  • Credit spread
  • Default
  • Default intensity
  • Jump-diffusion process
  • Spectral expansion
  • State dependent Lévy measure
  • Subordinator
  • Time change

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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