(551b) Hedging Energy Commodities for Flexible Fuel Operations

Operators of flexible fuel utilities are subject to substantial risk due to stochastic price uncertainty in the commodity markets. To reduce financial risk and increase return, operators manage a portfolio consisting of physical or otherwise beneficial ownership of the underlying commodities [2, 3, 6]. The coordinated management of the portfolio and the flexible fuel operation is the hedging problem considered in this paper. The results of the paper can be used either by the process operator directly to reduce financial risk, or by an energy banker to price a an ’energy swap’ to finance process operation.

The mathematical development is based on self-financing hedging portfolio consisting of the flexible fuel process, physical ownership of the underlying energy commodities, and a risk-free asset. The returns on portfolio assets include the stochastic yields on the underlying assets, convenience yields attributable to physical ownership of commodities, and the obligation to operate the process to meet known demand. Compared to conventional formulations available in the literature [1, 4, 5], the novel aspects of this formulation are the inclusion of a flexible fuel process with a first and second law consistent model, and the inclusion of convenience yield.

Following standard techniques, the feedback control strategy for the operation of a coordinated, optimal, risk-free hedge is found as the solution to a stochastic optimal control problem. The associated Hamilton-Jacobi-Bellman equation is solved using finite difference methods. Special consideration is given to the necessary boundary conditions, which appear to be novel. The solution is validated by an independent Monte-Carlo solution.

The control strategy consists of feedback rules for managing the hedging portfolio as a function of time-to-go and spot prices of the underlying commodities. Performance of the control strategy is demonstrated through extensive back-testing with real-world price data for coal and natural gas subject to trading and ownership constraints. The hedging error is quantified and discussed.

References

1. Fred Benth, Jurate Benth, and Steen Koekebakker. Stochastic Modeling of Electricity and Related Markets. World Scientific, 2008.

2. S.J. Deng and S.S. Oren. Electricity derivatives and risk management. Energy, 31(6-7):940–953, 2006.

3. M. Denton, A. Palmer, R. Masiello, and P. Skantze. Managing market risk in energy. Power Systems, IEEE Transactions on, 18(2):494–502, 2003.

4. Alexander Eydeland and Krzysztof Wolyniec. Energy and Power Risk Management: New Developments in Modeling, Pricing and Hedging. Wiley, 2003.

5. Hélyette Geman. Commodities and Commodity Derivatives: Modeling and Pricing for Agriculturals, Metals and Energy. Wiley, 2005.

6. Yanbo Jin and Philippe Jorion. Firm value and hedging: Evidence from u.s. oil and gas producers. Journal of Finance, 61(2):893–919, April 2006.