Time-Changed CIR Default Intensities with Two-Sided Mean-Reverting Jumps

The Annals of Applied Probability, 24(2), 811-856

31 Pages Posted: 9 Sep 2012 Last revised: 24 Jul 2014

See all articles by Rafael Mendoza-Arriaga

Rafael Mendoza-Arriaga

University of Texas at Austin - Department of Information, Risk and Operations Management

Vadim Linetsky

Northwestern University - Department of Industrial Engineering and Management Sciences

Date Written: February 24, 2014

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 of the diffusion state variable and default indicator process (X,D) in the diffusion intensity model and time change it with a Levy subordinator T. We then give a detailed characterization of the resulting time changed process (Xφ,Dφ)=(X(T),D(T)) as a Markovian Ito semimartingale and, in particular, 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. In particular, when X is a CIR diffusion, the default intensity of the subordinate model (SubCIR) turns out to be a jump-diffusion or a pure jump process with two-sided mean-reverting jumps that stays non-negative. The SubCIR default intensity model is fully analytically tractable by means of the explicitly computed eigenfunction expansion of the relevant semigroups. This allows explicit closed-form pricing of credit-sensitive securities.

Keywords: SubCIR, Subordinate CIR, semimartingale, subordination, Feller, semigroups, default intensity, bivariate process, default, credit risk

Suggested Citation

Mendoza-Arriaga, Rafael and Linetsky, Vadim, Time-Changed CIR Default Intensities with Two-Sided Mean-Reverting Jumps (February 24, 2014). The Annals of Applied Probability, 24(2), 811-856, Available at SSRN: https://ssrn.com/abstract=2143716 or http://dx.doi.org/10.2139/ssrn.2143716

Rafael Mendoza-Arriaga (Contact Author)

University of Texas at Austin - Department of Information, Risk and Operations Management ( email )

CBA 5.202
Austin, TX 78712
United States
5126321860 (Phone)

HOME PAGE: http://rafaelmendoza.org

Vadim Linetsky

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

Evanston, IL 60208-3119
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
138
Abstract Views
926
Rank
376,949
PlumX Metrics