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Small noise fluctuations of the CIR model driven by α-stable noises

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  • Ma, Chunhua
  • Yang, Xu

Abstract

The central limit theorems, the deviation inequality (and large deviation), and the moderate deviations for least squares estimators of parameters in the CIR type model driven byα-stable noises are established when the dispersion parameter ε→0 and the discrete observation frequency k→∞ simultaneously.

Suggested Citation

  • Ma, Chunhua & Yang, Xu, 2014. "Small noise fluctuations of the CIR model driven by α-stable noises," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 1-11.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:1-11
    DOI: 10.1016/j.spl.2014.07.001
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    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    2. Long, Hongwei & Shimizu, Yasutaka & Sun, Wei, 2013. "Least squares estimators for discretely observed stochastic processes driven by small Lévy noises," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 422-439.
    3. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    4. Long, Hongwei, 2009. "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2076-2085, October.
    5. Ma, Chunhua, 2010. "A note on "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises"," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1528-1531, October.
    6. repec:bla:jfinan:v:58:y:2003:i:2:p:753-778 is not listed on IDEAS
    7. Uchida, Masayuki, 2008. "Approximate martingale estimating functions for stochastic differential equations with small noises," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1706-1721, September.
    8. Masayuki Uchida & Nakahiro Yoshida, 2004. "Asymptotic Expansion for Small Diffusions Applied to Option Pricing," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 189-223, October.
    9. Gloter, Arnaud & Sørensen, Michael, 2009. "Estimation for stochastic differential equations with a small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 679-699, March.
    10. Masayuki Uchida, 2004. "Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 553-566, December.
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    Citations

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    Cited by:

    1. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    2. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140, arXiv.org, revised Feb 2019.
    3. Guangjun Shen & Qian Yu, 2019. "Least squares estimator for Ornstein–Uhlenbeck processes driven by fractional Lévy processes from discrete observations," Statistical Papers, Springer, vol. 60(6), pages 2253-2271, December.
    4. Qian Yu, 2021. "Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean for general Hurst parameter," Statistical Papers, Springer, vol. 62(2), pages 795-815, April.
    5. Yang, Xu, 2017. "Maximum likelihood type estimation for discretely observed CIR model with small α-stable noises," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 18-27.
    6. Yusuke Kaino & Masayuki Uchida, 2018. "Hybrid estimators for small diffusion processes based on reduced data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 745-773, October.

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