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On the speed towards the mean for continuous time autoregressive moving average processes with applications to energy markets

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  • Benth, Fred Espen
  • Taib, Che Mohd Imran Che

Abstract

We extend the concept of half life of an Ornstein–Uhlenbeck process to Lévy-driven continuous-time autoregressive moving average processes with stochastic volatility. The half life becomes state dependent, and we analyze its properties in terms of the characteristics of the process. An empirical example based on daily temperatures observed in Petaling Jaya, Malaysia, is presented, where the proposed model is estimated and the distribution of the half life is simulated. The stationarity of the dynamics yield futures prices which asymptotically tend to constant at an exponential rate when time to maturity goes to infinity. The rate is characterized by the eigenvalues of the dynamics. An alternative description of this convergence can be given in terms of our concept of half life.

Suggested Citation

  • Benth, Fred Espen & Taib, Che Mohd Imran Che, 2013. "On the speed towards the mean for continuous time autoregressive moving average processes with applications to energy markets," Energy Economics, Elsevier, vol. 40(C), pages 259-268.
    • Handle: RePEc:eee:eneeco:v:40:y:2013:i:c:p:259-268
    DOI: 10.1016/j.eneco.2013.07.007
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    References listed on IDEAS

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    8. Fred Espen Benth & Jurate Saltyte-Benth, 2005. "Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 53-85.
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    More about this item

    Keywords

    CARMA processes; Stationarity; Half life; Mean reversion;
    All these keywords.

    JEL classification:

    • Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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