(555f) Valuation and Optimal Operation of Energy Commodity Storage

Kantor, J. C., University of Notre Dame
Fan, F., University of Notre Dame

Energy commodity prices are influenced by supply, demand, and exogenous events. Stochastic prices introduce financial risks for the operators of energy storage facilities.  Integrating the financial and physical operations of an energy commodity storage mitigates the effect of price fluctuations caused by unbalanced supply and demand, and offers the energy storage facility owner/operator lower financial risk.

We proposed a storage model serving known demand to maximize the expected profit of a storage operation for a generic energy commodity such as coal, natural gas, or oil. The storage holds a finite inventory subject to bounds on the rate at which the energy commodity can be stored or recovered. We assume a finite convenience yield [3], [2], where convenience yield is defined as the additional value that accrues due to physical ownership of a commodity.

The mathematical model is derived following a dynamic programming procedure found in [5], [6], [7], and [8]. The model features a finite convenience yield and mean-reverting price model for a single energy commodity. The resulting Hamilton-Jacobi-Bellman (HJB) equation is obtained to solve for an optimal control strategy. A numerical solution is computed using finite differences and boundary conditions specific to this application. The model can be extended to price processes with jump diffusions.

Computational results demonstrate the incremental value of physical ownership of energy commodities. The valuation result is compared with that computed with a thresholding method [4]. Comparision demonstrates the value of solving for an optimal control using the dynamic programming. The models are calibrated to historical data, and validated using out-of-sample testing with historical data.


[1]   Shijie Deng. Stochastic models of energy commodity prices and their applications: Mean-reversion with jumps and spikes. working paper, University of California Energy Institute, February 2000.

[2]   Rajna Gibson and Eduardo S. Schwartz. Stochastic convenience yield and the pricing of oil contingent claims. The Journal of Finance, 45(3):959–976, 1990.

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

[4]   Stephen Boyd Jacob Mattingley, Yang Wang. Receding horizon control: automatic generation of high-speed solvers. IEEE control system magazine, pages 52–65, June 2011.

[5]   Robert C. Merton. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3:125–144, 1976.

[6]   Robert C. Merton. Continuous time finance. Blackwell publishers, 1990.

[7]   Matt Thompson, Matt Davison, and Henning Rasmussen. Valuation and optimal operation of electric power plants in competitive markets. Operations Research, 52(4):546–562, July–August 2004.

[8]   Matt Thompson, Matt Davison, and Henning Rasmussen. Natural gas storage valuation and optimization: A real options application. Naval Research Logistics, 56(3):226–238, 2009.



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