Stochastic models of electricity prices and risk premia in the PJM market

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Copyright: Xiao, Yuewen
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Abstract
With a main focus on risk premia in a US electricity market, we propose three stochastic models for electricity spot prices. Based on the proposed models, we derive closed-form pricing formulae for electricity forward contracts with the martingale approach and specify time-varying risk premia. Parameters are estimated with Kalman filters and variations. The thesis consists of three essays. The first essay deals with long-term electricity price modeling and a constant risk premium. We construct a jump-diffusion model with seasonality, mean-reversion, time-dependent jump intensity and heteroskedastic disturbance for the electricity spot prices, while keeping the analytical tractability of the futures prices. It is usually very difficult to derive closed-form futures pricing formula with existing jump-diffusion models which include GARCH effects. We find that the jump component plays a considerably larger role than the diffusion component in the variance of spot prices, and the jump intensity is much higher during summer and winter. The significance of the GARCH parameters reveals heteroskedasticity and persistent volatility in the price series. We explore the constant market price of risk (MPR) with different maturities, from one month up to five months. Our results also show that the market price of risk, while seasonal, is always negative. The second essay develops a jump-diffusion model for short-term electricity price series, where the heteroskedasticity disappears. The model not only takes seasonality, mean-reversion, and time-dependent jump intensity into account, but also allows the mean-reversion rates of the diffusion component and the jump component to be different. It is typical to assume that the diffusion component and the jump component share the same mean-reversion rate in literature. Our maximum likelihood estimates confirms that the jump component reverts to the long-term level with a faster speed than the diffusion component. Moreover, the rates of mean reversion for both the components under the risk-neutral measure are different from those under the physical measure. Most literature considers the jump risk premium constant. However, we find that both the jump risk premium and the diffusion risk premium are time-varying and state-dependent. Generally, the jump risk premium stays positive and remains larger than the diffusion risk premium. The third essay is concerned with a two-state regime-switching model. Electricity prices are divided into ``base" and ``spike" regimes. The base regime is characterised by a mean-reversion diffusion. The spike regime is a shift of the mean-reverting diffusion from the base regime for different parameters. Although most existing regime-switching autoregressive models assume homogenous transition probabilities, We allow the transition probabilities to be seasonal. Moreover, most existing models in electricity pricing assume that the switching mechanism only affects parameters in a model. However, we assume that the switching mechanism affects the model structure via the number of stochastic components (risk sources). As expected, the probability of staying in the base regime is much larger than in the spike regime and the probability of transiting into the spike regime is higher in winter and summer. The risk premium under the base regime is negatively correlated with the diffusion level with a negative intercept, while the risk premium on spikes is positively correlated with the size of the spike with a positive intercept.
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Author(s)
Xiao, Yuewen
Supervisor(s)
Colwell, David
Bhar, Ramaprasad
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Publication Year
2012
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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