Mathematics and Financial Economics

, Volume 13, Issue 2, pp 209–226 | Cite as

Barndorff-Nielsen and Shephard model: oil hedging with variance swap and option

  • Indranil SenGuptaEmail author
  • William Wilson
  • William Nganje


In this paper the Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for the oil commodity from the Bakken, a new region of oil extraction that is benefiting from fracking technology. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The results indicate that oil can be optimally hedged with the use of a combination of options and variance swaps. Theoretical results related to the variance process are established and implemented for the analysis of the variance swap. In this paper we also determined the optimal amount of the underlying oil commodity that has to be held for minimizing the hedging error. The model and analysis are used to numerically analyze hedging decisions for managing price risk in Bakken oil commodities. From the numerical results, a number of important features of the usefulness of the Barndorff-Nielsen and Shephard model are illustrated.


Oil commodity Barndorff-Nielsen and Shephard model Stochastic volatility Options and swaps Quadratic hedging 

JEL Classification

C02 D53 G10 Q02 



The authors would like to thank the anonymous reviewers for their careful reading of the manuscript and for suggesting points to improve the quality of the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNorth Dakota State UniversityFargoUSA
  2. 2.Department of Agribusiness and Applied EconomicsNorth Dakota State UniversityFargoUSA

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