A CHANGE OF MEASURE PRESERVING THE AFFINE STRUCTURE IN THE BARNDORFF-NIELSEN AND SHEPHARD MODEL FOR COMMODITY MARKETS

Fred Espen Benth () and Salvador Ortiz-Latorre ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 06, 1-40

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.

Keywords: Commodity markets; Barndorff-Nielsen and Shephard stochastic volatility model; change of measure; forward contracts; risk premium; generalized Riccati equations; affine processes (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024915500387

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