Pricing and Risk Management in Competitive Electricity Markets
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Electricity prices in competitive markets are extremely volatile with salient features such as mean-reversion and jumps and spikes. Modeling electricity spot prices is essential for asset and project valuation as well as risk management. I introduce the mean-reversion feature into a classical variance gamma model to model the electricity price dynamics as a mean-reverting variance gamma (MRVG) process. Derivative pricing formulae are derived through transform analysis and model parameters are estimated by the generalized method of moments and the Markov Chain Monte Carlo method. A real option approach is proposed to value a tolling contract incorporating operational characteristics of the generation asset and contractual constraints. Two simulation-based methods are proposed to solve the valuation problem. The effects of different electricity price assumptions on the valuation of tolling contracts are examined. Based on the valuation model, I also propose a heuristic scheme for hedging tolling contracts and demonstrate the validity of the hedging scheme through numerical examples. Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized ARCH (GARCH) models are widely used to model price volatility in financial markets. Considering a GARCH model with heavy-tailed innovations for electricity price, I characterize the limiting distribution of a Value-at-Risk (VaR) estimator of the conditional electricity price distribution, which corresponds to the extremal quantile of the conditional distribution of the GARCH price process. I propose two methods, the normal approximation method and the data tilting method, for constructing confidence intervals for the conditional VaR estimator and assess their accuracies by simulation studies. The proposed approach is applied to electricity spot price data taken from the Pennsylvania-New Jersey-Maryland market to obtain confidence intervals of the empirically estimated Value-at-Risk of electricity prices. Several directions that deserve further investigation are pointed out for future research.