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A Change Of Measure Preserving The Affine Structure In The Barndorff-Nielsen And Shephard Model For Commodity Markets

Author

Listed:
  • FRED ESPEN BENTH

    (Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, Oslo, N-0316, Norway)

  • SALVADOR ORTIZ-LATORRE

    (Department of Mathematics, University of Oslo, P. O. Box 1053, Blindern, Oslo, N-0316, Norway)

Abstract

For a commodity spot price dynamics given by an Ornstein–Uhlenbeck (OU) 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 are typically observed in energy markets. In particular, our pricing measure preserves the affine model structure and decomposes into a price and volatility risk premium. 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 explain 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.

Suggested Citation

  • Fred Espen Benth & Salvador Ortiz-Latorre, 2015. "A Change Of Measure Preserving The Affine Structure In The Barndorff-Nielsen And Shephard Model For Commodity Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-40.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:06:n:s0219024915500387
    DOI: 10.1142/S0219024915500387
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    Cited by:

    1. Ole E. Barndorff-Nielsen, 2016. "Assessing Gamma kernels and BSS/LSS processes," CREATES Research Papers 2016-09, Department of Economics and Business Economics, Aarhus University.

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