Hedging Price Risk for an Electricity Producer with Multistage Distributionally Robust Optimization
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In this thesis, we consider optimal hedging decisions for an electricity producer. In addition to account for uncertain prices and production, we let the underlying probability distribution in itself be subject to uncertainty. Distributional uncertainty is known as ambiguity, and is accounted for by applying a multistage distributionally robust optimization model. By modeling ambiguity as a so-called ambiguity set of possible probability distributions, the distributionally robust model finds the optimal hedging decision for the probability distribution in the ambiguity set that causes the most harm. We extend an existing framework for multistage distributionally robust optimization to incorporate risk aversion, using time consistent conditional value at risk as a risk measure. The input scenario tree is generated from a forecast fan with application of stochastic approximation. We find that the hedging strategy from the distributionally robust model outperforms a stochastic model under the worst case distribution from the ambiguity set, while it suffers only a slight reduction in performance when the distribution is correctly estimated. The risk is therefore reduced by applying a distributionally robust hedging model under ambiguity. Backtesting the hedging strategy on historical data from 2014 to 2017 shows that the distributionally robust model outperforms both the strategy from a stochastic model and a strategy where hedging is absent, in terms of mean profits. Our findings therefore suggest that distributional uncertainty should be accounted for when developing optimal hedging strategies for electricity producers.