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A pathwise inference method for the parameters of diffusion terms

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  • Nikolai Dokuchaev

Abstract

We consider inference of the parameters of the diffusion term for continuous time stochastic processes with a power-type dependence of the diffusion coefficient from the underlying process such as Cox–Ingersoll–Ross, CKLS, and similar processes. We suggest some original pathwise estimates for this coefficient and for the power index based on an analysis of an auxiliary continuous time complex-valued process generated by the underlying real-valued process. These estimates do not rely on the distribution of the underlying process and on a particular choice of the drift. Some numerical experiments are used to illustrate the feasibility of the suggested method.

Suggested Citation

  • Nikolai Dokuchaev, 2017. "A pathwise inference method for the parameters of diffusion terms," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 731-743, October.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:731-743
    DOI: 10.1080/10485252.2017.1367789
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    References listed on IDEAS

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    1. Gibbons, Michael R & Ramaswamy, Krishna, 1993. "A Test of the Cox, Ingersoll, and Ross Model of the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 619-658.
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    4. Lin-Yee Hin & Nikolai Dokuchaev, 2016. "Short Rate Forecasting Based On The Inference From The Cir Model For Multiple Yield Curve Dynamics," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-33, March.
    5. Chuong Luong & Nikolai Dokuchaev, 2016. "Modeling Dependency Of Volatility On Sampling Frequency Via Delay Equations," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-21, June.
    6. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    7. Nikolai Dokuchaev, 2015. "Modelling Possibility of Short-Term Forecasting of Market Parameters for Portfolio Selection," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 143-161, May.
    8. repec:adr:anecst:y:2013:i:109-110:p:2 is not listed on IDEAS
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. K. Fergusson & E. Platen, 2015. "Application Of Maximum Likelihood Estimation To Stochastic Short Rate Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-26, December.
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    12. Nikolai Dokuchaev, 2014. "Volatility estimation from short time series of stock prices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 373-384, June.
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    Cited by:

    1. Mishura, Yuliya & Ralchenko, Kostiantyn & Dehtiar, Olena, 2022. "Parameter estimation in CKLS model by continuous observations," Statistics & Probability Letters, Elsevier, vol. 184(C).

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