Levy driven Markov-modulated Ornstein-Uhlenbeck processes: application to Alberta electricity market
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2012-10-03
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Abstract
This thesis is a study of the distinctive stochastic properties exhibited in Alberta's electricity market. Electricity spot prices are notoriously difficult to model, which motivate us to develop new models. Our model combines the Ornstein-Uhlenbeck process for the spot dynamics of electricity with Markov-Modulated parameters. In this way, the model allows for Markov-Modulated mean-reversion rates and volatilities. Compared with the classical finance model, Markov-Modulated model or Markovian regime-switching models, by construction, should provide a better fit to volatile electricity spot prices. A brief overview of the history of Markov-Modulated models in finance theory, as well as the main contributions and contents of this thesis, is given in Chapter 1. Chapter 2 is the theoretical foundation of this thesis; in this chapter, we review some basic definitions and results on Markov process, Semi-Markov process, continuous time Markov chain, Levy processes and Ito's formula. In Chapter 3, we develop a new process called the Markov-Modulated Ornstein-Uhlenbeck process. We study all properties of this Markov-Modulated Ornstein-Uhlenbeck process. We build two models, geometric and arithmetic, for electricity spot price dynamics. In Chapter 4, using the models we described in Chapter 3, we give the pricing formulas for forwards and swaps contracts of electricity. Two approaches, geometric and arithmetic, are used to derive different types of pricing formulas using different properties of geometric and arithmetic models. Two specific Levy processes, NIG and CGMY are studied in detail for both geometric and arithmetic cases. Another main contribution of this thesis is given in Chapter 5, where we invoke the Markov-Modulated and Semi-Markov-Modulated volatilities together with electricity forward prices to get a generalization of the Black-76 formula to price European call options, for the cases with symmetric and non-symmetric transition rates between states, and with and without jumps in the forward dynamics. Simulation results for the models described in Chapter 3 are given in Chapter 6. Finally, daily average electricity spot market data from the Alberta electricity market for the period of January 1, 2000 to December 31, 2011 are studied in detail in Chapter 7. In Chapter 8, we conclude and propose future work.
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Mathematics, Mathematics
Citation
Zhao, K. (2012). Levy driven Markov-modulated Ornstein-Uhlenbeck processes: application to Alberta electricity market (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26752