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A closed-form solution for the price of cross-commodity electricity derivatives

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  • Tsitakis, D.
  • Xanthopoulos, S.
  • Yannacopoulos, A.N.

Abstract

We present a method for the valuation of two types of cross-commodity electricity options, European spark spread options and locational spread options. Since the underlying assets here are non-tradeable, the methodology of Black–Scholes–Merton cannot be directly applied. Nevertheless, assuming only absence of arbitrage we provide a closed-form analytic formula for the price of the derivatives in the case where the spot prices of the underlying process follow an exponential Ornstein–Uhlenbeck process.

Suggested Citation

  • Tsitakis, D. & Xanthopoulos, S. & Yannacopoulos, A.N., 2006. "A closed-form solution for the price of cross-commodity electricity derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 543-551.
    • Handle: RePEc:eee:phsmap:v:371:y:2006:i:2:p:543-551
    DOI: 10.1016/j.physa.2006.03.037
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    References listed on IDEAS

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    1. Horsley, Anthony & Wrobel, Andrew J., 2002. "Efficiency rents of pumped-storage plants and their uses for operation and investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 109-142, November.
    2. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    3. Spear, Stephen E., 2003. "The electricity market game," Journal of Economic Theory, Elsevier, vol. 109(2), pages 300-323, April.
    4. Anthony Horsley & Andrew J. Wrobel, 2002. "Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 503-537.
    5. Anthony Horsley & Andrew Wrobel, 2005. "Continuity of the equilibrium price density and its uses in peak-load pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 839-866, November.
    6. Lucia, Julio J. & Schwartz, Eduardo, 2000. "Electricity prices and power derivatives: Evidence from the Nordic Power Exchange," University of California at Los Angeles, Anderson Graduate School of Management qt12w8v7jj, Anderson Graduate School of Management, UCLA.
    7. Fred Espen Benth & Lars Ekeland & Ragnar Hauge & BjøRn Fredrik Nielsen, 2003. "A note on arbitrage-free pricing of forward contracts in energy markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(4), pages 325-336.
    8. Juri Hinz, 2003. "Modelling day-ahead electricity prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(2), pages 149-161.
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