The Annals of Applied Probability

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

Rafael Mendoza-Arriaga and Vadim Linetsky

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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 Lévy subordinator $\mathcal{T}$. We characterize the time-changed process $(X^{\phi}_{t},D^{\phi}_{t})=(X(\mathcal{T}_{t}),D(\mathcal{T}_{t}))$ as a Markovian–Itô 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.

Article information

Source
Ann. Appl. Probab. Volume 24, Number 2 (2014), 811-856.

Dates
First available in Project Euclid: 10 March 2014

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1394465372

Digital Object Identifier
doi:10.1214/13-AAP936

Mathematical Reviews number (MathSciNet)
MR3178498

Zentralblatt MATH identifier
1291.91225

Subjects
Primary: 91G40: Credit risk
Secondary: 60J75: Jump processes 91G30: Interest rates (stochastic models) 60G55: Point processes

Keywords
Default default intensity credit spread corporate bond credit derivative CIR process time change subordinator Bochner subordination jump-diffusion process state dependent Lévy measure spectral expansion

Citation

Mendoza-Arriaga, Rafael; Linetsky, Vadim. Time-changed CIR default intensities with two-sided mean-reverting jumps. Ann. Appl. Probab. 24 (2014), no. 2, 811--856. doi:10.1214/13-AAP936. http://projecteuclid.org/euclid.aoap/1394465372.


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