# Asma Khedher: Stationarity of Ornstein-Uhlenbeck processes with stochastic speed of mean reversion

Asma Khedher (Technische Universität München) holder et seminar med tittelen: Stationarity of Ornstein-Uhlenbeck processes with stochastic speed of mean reversion

Abstract: When modelling energy prices with the Ornstein-Uhlenbeck (OU) process, it was shown in Barlow, Gusev, and Lai [1] and Zapranis and Alexandridis [2] 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 generalised the OU process to allow for the speed of mean reversion to be stochastic. We suppose that the speed of mean-reversion is a Brownian stationary process. Then, we show the stationarity of the mean and variance of the OU process when the average speed of mean-reversion is suﬃciently larger than its variance. We further compute the chaos expansion of the generalised OU process and show that the kernel functions converge in norm as time tends to inﬁnity.

(Joint work with Fred Espen Benth)

References

[1] Barlow, M., Gusev. Y., and Lai, M. (2004). Calibration of multifactor models in electricity markets. International Journal of Theoretical and Applied Finance, 7, (2), pp. 101–120.

[2] Zapranis, A., Alexandridis, A. (2009). Weather derivatives pricing: modelling the seasonal residual variance of an Ornstein-Uhlenbeck temperature process with neural networks. Journal Neurocomputing, 73 (1-3), pp. 37–48.