IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i4d10.1007_s00362-023-01494-1.html
   My bibliography  Save this article

Least squares estimation for a class of uncertain Vasicek model and its application to interest rates

Author

Listed:
  • Chao Wei

    (Anyang Normal University)

Abstract

This paper addresses statistical inference in uncertain differential equations, focusing on parameter estimation for a class of uncertain Vasicek model with a small dispersion coefficient from discrete observations. Least squares estimators are obtained using a defined contrast function. The consistency and asymptotic distribution of these estimators are established. Numerical simulations and empirical analysis on real interest rate data highlight the efficacy of the proposed estimators and the methodology’s practicality in capturing interest rate dynamics.

Suggested Citation

  • Chao Wei, 2024. "Least squares estimation for a class of uncertain Vasicek model and its application to interest rates," Statistical Papers, Springer, vol. 65(4), pages 2441-2459, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01494-1
    DOI: 10.1007/s00362-023-01494-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-023-01494-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-023-01494-1?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    2. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Noorani, Idin & Mehrdoust, Farshid, 2022. "Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Chao Wei, 2021. "Parameter estimation for stochastic Lotka-Volterra model driven by small Lévy noises from discrete observations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(24), pages 6014-6023, November.
    6. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    7. Katsuto Tanaka & Weilin Xiao & Jun Yu, 2020. "Maximum Likelihood Estimation for the Fractional Vasicek Model," Econometrics, MDPI, vol. 8(3), pages 1-28, August.
    8. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, 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. Li, Yicun & Teng, Yuanyang, 2023. "Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Khalifa Es-Sebaiy & Mohammed Es.Sebaiy, 2021. "Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 409-436, June.
    3. Chuong Luong & Nikolai Dokuchaev, 2016. "Modeling Dependency Of Volatility On Sampling Frequency Via Delay Equations," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-21, June.
    4. Ben S. Bernanke & Vincent R. Reinhart & Brian P. Sack, 2004. "Monetary Policy Alternatives at the Zero Bound: An Empirical Assessment," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 35(2), pages 1-100.
    5. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    6. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    7. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    8. Gonçalo Jacinto & Patrícia A. Filipe & Carlos A. Braumann, 2022. "Profit Optimization of Cattle Growth with Variable Prices," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1917-1952, September.
    9. Olivier Le Courtois, 2022. "On the Diversification of Fixed Income Assets," Risks, MDPI, vol. 10(2), pages 1-21, February.
    10. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    11. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    12. Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2019. "Long-term swings and seasonality in energy markets," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1011-1023.
    13. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    14. João Nunes, 2011. "American options and callable bonds under stochastic interest rates and endogenous bankruptcy," Review of Derivatives Research, Springer, vol. 14(3), pages 283-332, October.
    15. Jorge Miguel Bravo, 2019. "Funding for longer lives. Retirement wallet and risk-sharing annuities," EKONOMIAZ. Revista vasca de Economía, Gobierno Vasco / Eusko Jaurlaritza / Basque Government, vol. 96(02), pages 268-291.
    16. Mahdavi, Mahnaz, 2008. "A comparison of international short-term rates under no arbitrage condition," Global Finance Journal, Elsevier, vol. 18(3), pages 303-318.
    17. Ilias Lekkos, 2003. "Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(5‐6), pages 799-828, June.
    18. Chang Shih-Chieh Bill & Lee Yen-Kuan, 2020. "Currency Uncertainty, Interest Guarantee, and Risk-Based Premiums in Life Insurance Guaranty Schemes," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-30, July.
    19. Piotr Komański & Oskar Sokoliński, 2015. "Least-Squares Monte Carlo Simulation for Time Value of Options and Guarantees Calculation," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 41.
    20. Sascha Meyer & Willi Schwarz, 2003. "A PDE based Implementation of the Hull&White Model for Cashflow Derivatives," Computational Statistics, Springer, vol. 18(3), pages 417-434, September.

    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:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01494-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.