IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v70y2016icp320-326.html
   My bibliography  Save this article

Long-term behavior of stochastic interest rate models with Markov switching

Author

Listed:
  • Zhang, Zhenzhong
  • Tong, Jinying
  • Hu, Liangjian

Abstract

In this paper, we consider the long time behavior of Cox–Ingersoll–Ross (CIR) interest rate model with Markov switching. Using the ergodic theory of switching diffusions, we show that CIR model with Markov switching has a unique stationary distribution. Furthermore, we prove that the sequence X¯t:=1t∫0tXsds converges almost surely. As a by-product, we find that the marginal stationary distribution for CIR model with Markov switching can be determined uniquely by its moments.

Suggested Citation

  • Zhang, Zhenzhong & Tong, Jinying & Hu, Liangjian, 2016. "Long-term behavior of stochastic interest rate models with Markov switching," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 320-326.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:320-326
    DOI: 10.1016/j.insmatheco.2016.06.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668715303218
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2016.06.017?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. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Deelstra, G. & Delbaen, F., 1995. "Long-term returns in stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 163-169, October.
    3. Smith, Daniel R, 2002. "Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 183-197, April.
    4. Clifford A. Ball & Walter N. Torous, 1999. "The Stochastic Volatility of Short‐Term Interest Rates: Some International Evidence," Journal of Finance, American Finance Association, vol. 54(6), pages 2339-2359, December.
    5. Bao, Jianhai & Yuan, Chenggui, 2013. "Long-term behavior of stochastic interest rate models with jumps and memory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 266-272.
    6. Zhao, Juan, 2009. "Long time behaviour of stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 459-463, June.
    7. Griselda Deelstra & Freddy Delbaen, 1995. "Long-term returns in stochastic interest rate models," ULB Institutional Repository 2013/7578, ULB -- Universite Libre de Bruxelles.
    8. Griselda Deelstra & Freddy Delbaen, 1995. "Long-term returns in stochastic interest rate models: convergence in law," ULB Institutional Repository 2013/7580, ULB -- Universite Libre de Bruxelles.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ji, Huijie & Xi, Fubao, 2022. "The tail behavior of jump-diffusion Cox–Ingersoll–Ross processes with regime-switching," Statistics & Probability Letters, Elsevier, vol. 181(C).

    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. Bao, Jianhai & Yuan, Chenggui, 2013. "Long-term behavior of stochastic interest rate models with jumps and memory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 266-272.
    2. Jan de Kort, 2018. "A note on the long rate in factor models of the term structure," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 656-667, April.
    3. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.
    4. Griselda Deelstra, 2000. "Long-term returns in stochastic interest rate models: applications," ULB Institutional Repository 2013/7590, ULB -- Universite Libre de Bruxelles.
    5. Kalimipalli, Madhu & Susmel, Raul, 2004. "Regime-switching stochastic volatility and short-term interest rates," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 309-329, June.
    6. Duc, Luu Hoang & Tran, Tat Dat & Jost, Jürgen, 2018. "Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3253-3272.
    7. Sun, Licheng, 2005. "Regime shifts in interest rate volatility," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 418-434, June.
    8. Federico Flore & Giovanna Nappo, 2018. "A Feynman-Kac type formula for a fixed delay CIR model," Papers 1806.00997, arXiv.org.
    9. Daniel R. Smith & Christophe Parignon, 2004. "Modeling Yield-Factor Volatility," Econometric Society 2004 Australasian Meetings 307, Econometric Society.
    10. Zhao, Juan, 2009. "Long time behaviour of stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 459-463, June.
    11. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    12. Gabriel Faraud & Stéphane Goutte, 2014. "Bessel Bridges Decomposition with Varying Dimension: Applications to Finance," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1375-1403, December.
    13. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    14. Christiansen, Charlotte, 2008. "Level-ARCH short rate models with regime switching: Bivariate modeling of US and European short rates," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 925-948, December.
    15. Lourdes Gómez-Valle & Julia Martínez-Rodríguez, 2010. "Improving the term structure of interest rates: two-factor models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(3), pages 275-287.
    16. David Markantonis & G.-Fivos Sargentis & Panayiotis Dimitriadis & Theano Iliopoulou & Aimilia Siganou & Konstantina Moraiti & Maria Nikolinakou & Ilias Taygetos Meletopoulos & Nikos Mamassis & Demetri, 2023. "Stochastic Evaluation of the Investment Risk by the Scale of Water Infrastructures—Case Study: The Municipality of West Mani (Greece)," World, MDPI, vol. 4(1), pages 1-20, January.
    17. Hideyuki Takamizawa, 2015. "Predicting Interest Rate Volatility Using Information on the Yield Curve," International Review of Finance, International Review of Finance Ltd., vol. 15(3), pages 347-386, September.
    18. Travis Sapp, 2009. "Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter," Review of Quantitative Finance and Accounting, Springer, vol. 33(4), pages 303-326, November.
    19. repec:wyi:journl:002109 is not listed on IDEAS
    20. Perignon, Christophe & Smith, Daniel R., 2007. "Yield-factor volatility models," Journal of Banking & Finance, Elsevier, vol. 31(10), pages 3125-3144, October.
    21. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.

    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:insuma:v:70:y:2016:i:c:p:320-326. 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/locate/inca/505554 .

    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.