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Weak Stationarity of Ornstein-Uhlenbeck Processes with Stochastic Speed of Mean Reversion

In: The Fascination of Probability, Statistics and their Applications

Author

Listed:
  • Fred Espen Benth

    (University of Oslo, Department of Mathematics)

  • Asma Khedher

    (Technische Universität München, Chair of Mathematical Finance)

Abstract

When modeling energy prices with the Ornstein-Uhlenbeck process, it was shown in Barlow et al. [2] and Zapranis and Alexandris [21] that there is a large uncertainty attached to the estimation of the speed of mean-reversion and that it is not constant but may vary considerably over time. In this paper we generalise the Ornstein-Uhlenbeck process to allow for the speed of mean reversion to be stochastic. We suppose that the mean-reversion is a Brownian stationary process. We apply Malliavin calculus in our computations and we show that this generalised Ornstein-Uhlenbeck process is stationary in the weak sense. Moreover we compute the instantaneous rate of change in the mean and in the squared fluctuations of the genaralised Ornstein-Uhlenbeck process given its initial position. Finally, we derive the chaos expansion of this generalised Ornstein-Uhlenbeck process.

Suggested Citation

  • Fred Espen Benth & Asma Khedher, 2016. "Weak Stationarity of Ornstein-Uhlenbeck Processes with Stochastic Speed of Mean Reversion," Springer Books, in: Mark Podolskij & Robert Stelzer & Steen Thorbjørnsen & Almut E. D. Veraart (ed.), The Fascination of Probability, Statistics and their Applications, pages 153-189, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-25826-3_8
    DOI: 10.1007/978-3-319-25826-3_8
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