Barndorff-Nielsen and Shephard model for hedging energy with quantity risk

Abstract

In this paper, the Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy in the presence of quantity risk for oil produced in the Bakken, a new region of oil extraction that is benefiting from fracking technology. Hedging and price risk management become much more involved with the inclusion of quantity risk. Explorers and drillers have uncertainty on the quantity of oil that would be extracted, and governments have uncertainty of the quantity of oil that will be extracted, sold, and available for imposing tax regimes. One of the main assumptions typically made in a portfolio model of hedging is that the quantity of inventory or demand is known. This is inappropriate in many hedging situations. Quantity risk compounds the difficulty of determining the optimal size of the position under both price and production risk. In this paper, we provide a novel way of handling the quantity risk in connection with the BN-S model. The model is analyzed as a quadratic hedging problem and related analytical results are developed. The results indicate that oil can be optimally hedged with a combination of variance swaps and options. For various quantity risks, the model is implemented to analyze hedging decisions numerically for managing price risk in the Bakken oil commodities.