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Exponential ergodicity of an affine two-factor model based on the α-root process

Part of: Ergodic theory Markov processes

Published online by Cambridge University Press:  17 November 2017

Peng Jin ,
Jonas Kremer  and
Barbara Rüdiger
Peng Jin*
Affiliation:
Bergische Universität Wuppertal
Jonas Kremer*
Affiliation:
Bergische Universität Wuppertal
Barbara Rüdiger*
Affiliation:
Bergische Universität Wuppertal
*
* Postal address: Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42119 Wuppertal, Germany.
* Postal address: Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42119 Wuppertal, Germany.
* Postal address: Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42119 Wuppertal, Germany.
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Abstract

We study an affine two-factor model introduced by Barczy et al. (2014). One component of this two-dimensional model is the so-called α-root process, which generalizes the well-known Cox–Ingersoll–Ross process. In the α = 2 case, this two-factor model was used by Chen and Joslin (2012) to price defaultable bonds with stochastic recovery rates. In this paper we prove exponential ergodicity of this two-factor model when α ∈ (1, 2). As a possible application, our result can be used to study the parameter estimation problem of the model.

Keywords

Affine processexponential ergodicityα-root processtransition densityFoster–Lyapunov function

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces 37A25: Ergodicity, mixing, rates of mixing
Secondary: 60J35: Transition functions, generators and resolvents 60J75: Jump processes
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 4 , December 2017 , pp. 1144 - 1169
Copyright
Copyright © Applied Probability Trust 2017 

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