Moments and ergodicity of the jump-diffusion CIR process

Jin, Peng; Kremer, Jonas; Rüdiger, Barbara

doi:10.1080/17442508.2019.1576686

Cited by 13 publications

(10 citation statements)

References 22 publications

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“…More precisely, based on the representation by strong solutions of stochastic differential equations, ergodicity was studied in [30] for different Wasserstein distances. By using regularity of transition densities with respect to the Lebesgue measure combined with the Meyn-and-Tweedie stability theory the ergodicity in total variation distances has been studied in [3,27,38,37,53,29]. Finally, coupling techniques for affine processes are studied in [59,52].…”

Section: Below Then the Following Holds Truementioning

confidence: 99%

Stationary Covariance Regime for Affine Stochastic Covariance Models in Hilbert Spaces

Friesen¹,

Karbach²

2022

Preprint

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We study the long-time behavior of affine processes on positive self-adjoiont Hilbert-Schmidt operators which are of pure-jump type, conservative and have finite second moment. For subcritical processes we prove the existence of a unique limit distribution and construct the corresponding stationary affine process. Moreover, we obtain an explicit convergence rate of the underlying transition kernels to the limit distribution in the Wasserstein distance of order p ∈ [1, 2] and provide explicit formulas for the first two moments of the limit distribution. We apply our results to the study of infinite-dimensional affine stochastic covariance models in the stationary covariance regime, where the stationary affine process models the instantaneous covariance process. In this context we investigate the behavior of the implied forward volatility smile for large forward dates in a geometric affine forward curve model used for the modeling of forward curve dynamics in fixed income or commodity markets formulated in the Heath-Jarrow-Morton-Musiela framework.

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Section: Below Then the Following Holds Truementioning

confidence: 99%

Stationary Covariance Regime for Affine Stochastic Covariance Models in Hilbert Spaces

Friesen¹,

Karbach²

2022

Preprint

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“…In this special one-dimensional case [53] could also establish ergodicity under log moments and geometric ergodicity under the finiteness of κ > 0 moments and for J being an infinite activity subordinator, i.e. only having state-independent jumps.…”

Section: Its Laplace Transform For Anymentioning

confidence: 99%

“…• For K = R + [52,53] prove Harris recurrence and exponential ergodicity for the basic affine jump-diffusion, which arises as a default intensity model in credit risk [26], and slight extensions. These processes may not have state-dependent jumps.…”

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confidence: 99%

Geometric ergodicity of affine processes on cones

Mayerhofer

Stelzer

Vestweber

2020

Stochastic Processes and their Applications

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For affine processes on finite-dimensional cones, we give criteria for geometric ergodicitythat is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of the limiting distribution, where we exploit the crucial affine property, and finite moments, where we invoke the polynomial property of affine semigroups. Furthermore, we elaborate sufficient conditions for aperiodicity and irreducibility. Our results are applicable to Wishart processes with jumps on the positive semidefinite matrices, continuous-time branching processes with immigration in high dimensions, and classical termstructure models for credit and interest rate risk.

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“…Proof. First we recall that since the jump-type CIR process X b = (X b t ) t∈R + is an affine process, the corresponding characteristic function of X b t = X b t (0, y 0 ) is of exponential-affine form (see page 287 and 288 of [26], Section 3 of [27] or Section 4.1 of [18]). That is, for all…”

Section: Expansion Of the Log-likelihood Ratiomentioning

confidence: 99%

Local asymptotic properties for the growth rate of a jump-type CIR process

Alaya,

Kebaier,

Pap

et al. 2019

Preprint

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In this paper, we consider a one-dimensional jump-type Cox-Ingersoll-Ross process driven by a Brownian motion and a subordinator, whose growth rate is a unknown parameter. The Lévy measure of the subordinator is finite or infinite. Considering the process observed continuously or discretely at high frequency, we derive the local asymptotic properties for the growth rate in both ergodic and non-ergodic cases. Three cases are distinguished: subcritical, critical and supercritical. Local asymptotic normality (LAN) is proved in the subcritical case, local asymptotic quadraticity (LAQ) is derived in the critical case, and local asymptotic mixed normality (LAMN) is shown in the supercritical case. To do so, techniques of Malliavin calculus and a subtle analysis on the jump structure of the subordinator involving the amplitude of jumps and number of jumps are essentially used.

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Moments and ergodicity of the jump-diffusion CIR process

Cited by 13 publications

References 22 publications

Stationary Covariance Regime for Affine Stochastic Covariance Models in Hilbert Spaces

Stationary Covariance Regime for Affine Stochastic Covariance Models in Hilbert Spaces

Geometric ergodicity of affine processes on cones

Local asymptotic properties for the growth rate of a jump-type CIR process

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