IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v187y2025ics030441492500105x.html
   My bibliography  Save this article

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

Author

Listed:
  • Ben Alaya, Mohamed
  • Kebaier, Ahmed
  • Pap, Gyula
  • Tran, Ngoc Khue

Abstract

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 an unknown parameter. 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. 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 obtain these results, 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.

Suggested Citation

  • Ben Alaya, Mohamed & Kebaier, Ahmed & Pap, Gyula & Tran, Ngoc Khue, 2025. "Local asymptotic properties for the growth rate of a jump-type CIR process," Stochastic Processes and their Applications, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:spapps:v:187:y:2025:i:c:s030441492500105x
    DOI: 10.1016/j.spa.2025.104664
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441492500105X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104664?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Clément, Emmanuelle & Gloter, Arnaud, 2015. "Local Asymptotic Mixed Normality property for discretely observed stochastic differential equations driven by stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2316-2352.
    2. Reiichiro Kawai, 2013. "Local Asymptotic Normality Property for Ornstein–Uhlenbeck Processes with Jumps Under Discrete Sampling," Journal of Theoretical Probability, Springer, vol. 26(4), pages 932-967, December.
    3. Keller-Ressel, Martin & Mijatović, Aleksandar, 2012. "On the limit distributions of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2329-2345.
    4. Ngoc Khue Tran, 2017. "LAN property for an ergodic Ornstein–Uhlenbeck process with Poisson jumps," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 7942-7968, August.
    5. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    6. Ludger Overbeck, 1998. "Estimation for Continuous Branching Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 111-126, March.
    7. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    8. Barczy, Mátyás & Ben Alaya, Mohamed & Kebaier, Ahmed & Pap, Gyula, 2018. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1135-1164.
    9. Jorge A. León & Reyla Navarro & David Nualart, 2003. "An Anticipating Calculus Approach to the Utility Maximization of an Insider," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 171-185, January.
    10. Mohamed Ben Alaya & Ahmed Kebaier & Ngoc Khue Tran, 2020. "Local asymptotic properties for Cox‐Ingersoll‐Ross process with discrete observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1401-1464, December.
    11. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140, arXiv.org, revised Feb 2019.
    12. van Zanten, Harry, 2000. "A multivariate central limit theorem for continuous local martingales," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 229-235, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2016. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Papers 1609.05865, arXiv.org, revised Aug 2017.
    2. Mohamed Ben Alaya & Ahmed Kebaier & Ngoc Khue Tran, 2020. "Local asymptotic properties for Cox‐Ingersoll‐Ross process with discrete observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1401-1464, December.
    3. Barczy, Mátyás & Ben Alaya, Mohamed & Kebaier, Ahmed & Pap, Gyula, 2018. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1135-1164.
    4. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140, arXiv.org, revised Feb 2019.
    5. Jakobsen, Nina Munkholt & Sørensen, Michael, 2019. "Estimating functions for jump–diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3282-3318.
    6. Friesen, Martin & Jin, Peng & Rüdiger, Barbara, 2020. "Existence of densities for multi-type continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5426-5452.
    7. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2015. "Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model," Papers 1509.08869, arXiv.org, revised May 2018.
    8. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2013. "Stationarity and ergodicity for an affine two factor model," Papers 1302.2534, arXiv.org, revised Sep 2013.
    9. Cheng, Yuzhong & Hufnagel, Nicole & Masuda, Hiroki, 2024. "Estimation of ergodic square-root diffusion under high-frequency sampling," Econometrics and Statistics, Elsevier, vol. 32(C), pages 73-87.
    10. Alfonsi, Aurélien & Kebaier, Ahmed & Rey, Clément, 2016. "Maximum likelihood estimation for Wishart processes," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3243-3282.
    11. Martin Friesen & Sven Karbach, 2024. "Stationary covariance regime for affine stochastic covariance models in Hilbert spaces," Finance and Stochastics, Springer, vol. 28(4), pages 1077-1116, October.
    12. Matyas Barczy & Gyula Pap, 2013. "Asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations," Papers 1310.4783, arXiv.org, revised Jun 2015.
    13. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2013. "Parameter estimation for a subcritical affine two factor model," Papers 1302.3451, arXiv.org, revised Apr 2014.
    14. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org, revised Jul 2019.
    15. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    16. Carlos Escudero & Sandra Ranilla-Cortina, 2020. "Optimal Portfolios for Different Anticipating Integrals under Insider Information," Mathematics, MDPI, vol. 9(1), pages 1-19, December.
    17. Giesecke, K. & Schwenkler, G., 2019. "Simulated likelihood estimators for discretely observed jump–diffusions," Journal of Econometrics, Elsevier, vol. 213(2), pages 297-320.
    18. Aït-Sahalia, Yacine & Park, Joon Y., 2016. "Bandwidth selection and asymptotic properties of local nonparametric estimators in possibly nonstationary continuous-time models," Journal of Econometrics, Elsevier, vol. 192(1), pages 119-138.
    19. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    20. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:187:y:2025:i:c:s030441492500105x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.