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

Fred Espen Benth () and Asma Khedher ()
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Fred Espen Benth: University of Oslo, Department of Mathematics
Asma Khedher: Technische Universität München, Chair of Mathematical Finance

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 153-189 from Springer

Abstract: 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.

Keywords: Ornstein-Uhlenbeck processes; Mean reversion; Stationarity (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-25826-3_8

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DOI: 10.1007/978-3-319-25826-3_8

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