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A change of measure preserving the affine structure in the BNS model for commodity markets


  • Fred Espen Benth
  • Salvador Ortiz-Latorre


For a commodity spot price dynamics given by an Ornstein-Uhlenbeck process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for change of level and speed in the mean reversion of both the price and the volatility. The risk premium is derived in the case of arithmetic and geometric spot price processes, and it is demonstrated that we can provide flexible shapes that is typically observed in energy markets. In particular, our pricing measure preserves the affine model structure and decomposes into a price and volatility risk premium, and in the geometric spot price model we need to resort to a detailed analysis of a system of Riccati equations, for which we show existence and uniqueness of solution and asymptotic properties that explains the possible risk premium profiles. Among the typical shapes, the risk premium allows for a stochastic change of sign, and can attain positive values in the short end of the forward market and negative in the long end.

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  • Fred Espen Benth & Salvador Ortiz-Latorre, 2014. "A change of measure preserving the affine structure in the BNS model for commodity markets," Papers 1403.5236,
  • Handle: RePEc:arx:papers:1403.5236

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    References listed on IDEAS

    1. Fred Espen Benth & Salvador Ortiz-Latorre, 2013. "A pricing measure to explain the risk premium in power markets," Papers 1308.3378,
    2. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    3. Benth, Fred Espen & Cartea, Álvaro & Kiesel, Rüdiger, 2008. "Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2006-2021, October.
    4. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    5. Kolos, Sergey P. & Ronn, Ehud I., 2008. "Estimating the commodity market price of risk for energy prices," Energy Economics, Elsevier, vol. 30(2), pages 621-641, March.
    6. Kallsen, Jan & Muhle-Karbe, Johannes, 2010. "Exponentially affine martingales, affine measure changes and exponential moments of affine processes," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 163-181, February.
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