Dynamic Risk Management of Commodity Operations: Model and Analysis

Abstract

We consider the dynamic risk management problem for a commodity processor facing risk costs. The firm procures an input commodity and processes it to produce an output commodity over a multi-period horizon. 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 instruments to manage the commodity price risk, but cannot hedge the risk completely. Using the concept of conditional risk mappings, we extend the single period conditional value at risk (CVaR) measure to a dynamic setting and ensure a time-consistent representation of the firm's risk management objective. In a partially complete market framework, we show that the optimal financial trading policy is a CVaR-replicating portfolio. Contingent on optimal financial trading, we show that the optimal procurement and processing policies are characterized by price and horizon dependent inventory thresholds. We show, analytically, that the procurement threshold increases with risk costs during the horizon. Our numerical studies show that optimizing a time-consistent risk measure results in better risk control over the entire horizon when compared to optimizing the CVaR of total profits. We also find that myopic and risk-neutral optimal policies are poor substitutes for the optimal risk management policy, especially when the firm faces significant risk costs.

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