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A pseudo-likelihood estimator of the Ornstein–Uhlenbeck parameters from suprema observations

Author

Listed:
  • Christophette Blanchet-Scalliet

    (Universite Claude Bernard Lyon 1, Université Jean Monnet)

  • Diana Dorobantu

    (Université Claude Bernard Lyon 1)

  • Benoit Nieto

    (Universite Claude Bernard Lyon 1, Université Jean Monnet)

Abstract

In this paper, we propose an estimator for the Ornstein–Uhlenbeck parameters based on observations of its supremum. We derive an analytic expression for the supremum density. Making use of the pseudo-likelihood method based on the supremum density, our estimator is constructed as the maximal argument of this function. Using weak-dependency results, we prove some statistical properties on the estimator such as consistency and asymptotic normality. Finally, we apply our estimator to simulated and real data.

Suggested Citation

  • Christophette Blanchet-Scalliet & Diana Dorobantu & Benoit Nieto, 2024. "A pseudo-likelihood estimator of the Ornstein–Uhlenbeck parameters from suprema observations," Statistical Inference for Stochastic Processes, Springer, vol. 27(2), pages 407-425, July.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:2:d:10.1007_s11203-024-09307-4
    DOI: 10.1007/s11203-024-09307-4
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    References listed on IDEAS

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    1. Emmanuel Gobet & Gustaw Matulewicz, 2017. "Parameter estimation of Ornstein–Uhlenbeck process generating a stochastic graph," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 211-235, July.
    2. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. 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.
    5. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
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