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

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  • 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
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    References listed on IDEAS

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    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..
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    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. Griselda Deelstra & Freddy Delbaen, 1995. "Long-term returns in stochastic interest rate models," ULB Institutional Repository 2013/7578, ULB -- Universite Libre de Bruxelles.
    6. 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.
    7. Zhao, Juan, 2009. "Long time behaviour of stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 459-463, June.
    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.
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    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).
    2. Abhishek Pal Majumder, 2024. "Long time behavior of semi-Markov modulated perpetuity and some related processes," Papers 2410.15824, arXiv.org.

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