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Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent Chan–Karolyi–Longstaff–Sanders and Vasicek Models

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  • Yifan Bai

    (Peking University)

  • Xing Huang

    (Tianjin University)

Abstract

In this paper, Wang’s log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the Chan–Karolyi–Longstaff–Sanders (CKLS) model, where the diffusion coefficient is a power function of order $$\theta $$ θ with $$\theta \in [\frac{1}{2},1)$$ θ ∈ [ 1 2 , 1 ) ; the other one is the Vasicek model, where the diffusion coefficient only depends on distribution. Both models in the distribution-independent case can be used to characterize the interest rate in mathematical finance.

Suggested Citation

  • Yifan Bai & Xing Huang, 2023. "Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent Chan–Karolyi–Longstaff–Sanders and Vasicek Models," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1902-1921, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01210-z
    DOI: 10.1007/s10959-022-01210-z
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    References listed on IDEAS

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    1. Wang, Feng-Yu, 2018. "Distribution dependent SDEs for Landau type equations," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 595-621.
    2. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Jianhai Bao & Xing Huang, 2022. "Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1187-1215, June.
    5. Jean-Francois Chassagneux & Antoine Jacquier & Ivo Mihaylov, 2014. "An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients," Papers 1405.3561, arXiv.org, revised Apr 2016.
    6. 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.
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