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Tail probabilities of solutions to a generalized Ait-Sahalia interest rate model

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  • Dung, Nguyen Tien

Abstract

In this paper we consider a generalized Ait-Sahalia interest rate model. We first extend the space of admissible parameters that ensures the existence of a unique positive solution to the model. Then, we provide an explicit estimate for tail probabilities of solutions.

Suggested Citation

  • Dung, Nguyen Tien, 2016. "Tail probabilities of solutions to a generalized Ait-Sahalia interest rate model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 98-104.
    • Handle: RePEc:eee:stapro:v:112:y:2016:i:c:p:98-104
    DOI: 10.1016/j.spl.2016.01.026
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    3. 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..
    4. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," The Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    5. Gallant, A. Ronald & Tauchen, George, 1997. "Estimation Of Continuous-Time Models For Stock Returns And Interest Rates," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 135-168, January.
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    Cited by:

    1. Emmanuel Coffie, 2021. "Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations," Papers 2103.07651, arXiv.org, revised Jul 2021.
    2. Emmanuel Coffie, 2021. "Numerical approximation of hybrid Poisson-jump Ait-Sahalia-type interest rate model with delay," Papers 2107.03712, arXiv.org, revised Jul 2021.
    3. Kęstutis Kubilius & Aidas Medžiūnas, 2020. "Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient," Mathematics, MDPI, vol. 9(1), pages 1-14, December.
    4. Nguyen, Tien Dung, 2018. "Tail estimates for exponential functionals and applications to SDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4154-4170.

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