Mathematical Methods of Operations Research

, Volume 64, Issue 2, pp 187–209 | Cite as

Valuing virtual production capacities on flow commodities

  • Juri Hinz
Original Article


As a result of storability restrictions, the price risk management of flow commodities (such as natural gas, oil, and electrical power) is by no means a trivial matter.To protect price spikes, consumers purchase diverse swing-type contracts, whereas contract writers try to hedge themselves by appropriate physical assets, for instance, using storage utilities, through transmission and/or production capacities. However, the correct valuation of such contacts and their physical counterparts is still under lively debate. In this approach, an axiomatic setting to discuss price dynamics for flow commodity contracts is suggested. By means of a minimal set of reasonable assumptions we suggest a framework where the standard change-of-numeraire transformation converts a flow commodity market into a market consisting of zero bonds and some additional risky asset. Utilizing this structure, we apply the toolkit of interest rate theory to price the availability of production capacity on a flow commodity.


Swing option Electricity risk Energy economics Futures markets Power derivatives 


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  1. Barlow MT (2002) A diffusion model for electricity prices. Math Finan 12:287–298CrossRefzbMATHGoogle Scholar
  2. Björk T (1996) Interest rate theory. Lecture Notes in Mathematics, vol 1656, Springer, Berlin Heidelberg New YorkGoogle Scholar
  3. Brennan MJ (1958) The supply of storage. Am Econ Rev 41:50–72Google Scholar
  4. Carmona R, Durrleman V (2003) Pricing and hedging spread options. SIAM Rev 45, 627–685CrossRefMathSciNetzbMATHGoogle Scholar
  5. Fama EF, French KR (1987) Commodity future prices: some evidence on forecast power, premiums, and the theory of storage. J Bus 60 (1):55–73CrossRefGoogle Scholar
  6. Burger M, Klar B, Müller A, Schindlmayr G (2003) A spot market model for the pricing of derivatives in electricity markets. Quant Finan 4:109–122CrossRefGoogle Scholar
  7. Eydeland A, Geman H (1998) Pricing power derivatives, risk, 11 (10):71–73Google Scholar
  8. Eydeland A, Geman H (2003) Fundamentals of electricity Derivatives. Energy modelling and the management of uncertainty, Risk publications, chap. 3, 35–43Google Scholar
  9. Geman H, El Karoui N, Rochet JC (1995) Changes of numeraire, changes of probability measure and option pricing. J Appl Prob 32:443–458CrossRefMathSciNetzbMATHGoogle Scholar
  10. Gibson R, Schwartz ES (1990) Stochastic convenience yield and pricing of oil contingent claims. J Finan 45(3):959–976CrossRefGoogle Scholar
  11. Hinz J, von Grafenstein L, Verschuere M, Wilhelm M (2005) Pricing electricity risk by interest rate methods. Quant Financ 5(1):49–60CrossRefzbMATHGoogle Scholar
  12. Hinz J (2003) Modelling day-ahead electricity prices. Appl Mathel Finan 10(2):149–161CrossRefMathSciNetzbMATHGoogle Scholar
  13. Karatzas I, Shreve SE (1997) Brownian motion and stochastic calculus, 2nd edn., Springer, Berlin Heidelberg New YorkGoogle Scholar
  14. Karatzas I, Shreve SE (1998) Methods of Mathematical Finance. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  15. Schwartz ES, Lucia JJ (2002) Electricity prices and power derivatives. Evidence from the Nordic Power exchange. Rev Deriv Res 5(1):5–50CrossRefzbMATHGoogle Scholar
  16. Miltersen KR, Schwartz ES (1998) Pricing of options on commodity futures with stochastic term structures of convenience yields and interest rates. J Finan Quant Anal 33(1):33–59CrossRefGoogle Scholar
  17. Musiela M, Rutkowski M (1997) Martingale Methods in Financial Modelling. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  18. Schwartz ES (1997) The stochastic behavior of commodity prices: implication for valuation and hedging. J Finan 52:922–973CrossRefGoogle Scholar
  19. Rogers LCG, Williams D (1994) Diffusions, markov processes and martingales, vol 2, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  20. Schwartz ES, Lucia JJ (2002) Electricity prices and power derivatives. Evidence from the Nordic Power Exchange. Rev Deriv Res 5(1):5–50CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institute for Operations Research and RiskLab ETH ZentrumZurichSwitzerland

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