Dynamic Risk Management of Commodity Operations: Model and Analysis

We consider the dynamic risk management problem for a commodity processor in a multi-period setting. The firm procures an input commodity and processes it to produce an output commodity. The processed commodity is sold using forward contracts while the input itself can be traded at the end of the horizon. The firm can also trade financial derivative instruments to manage the commodity price risk. We propose a dynamic risk measure DCVaR, based on the conditional value at risk (CVaR), to model the firm’s risk aversion in a time-consistent manner over the planning horizon. We obtain the optimal procurement, processing and financial trading policies by formulating the risk management problem as a stochastic dynamic program. We show that the optimal operational policies procurement and processing are characterized by price dependent inventory thresholds and conditional on optimal financial hedging decisions, the operational policies can be calculated without knowing the details of the financial hedging itself. However, these optimal thresholds are hard to compute and we develop efficient heuristics to obtain the operational and financial decisions in each period. Using numerical studies, we show that a) these heuristics are near optimal and b) optimizing a time-consistent risk measure provides a better mean-risk tradeoff for the total profits and reduces the probability of extreme losses over the entire horizon, compared to optimizing the CVaR of total profits.