Sankhya B

, Volume 81, Issue 1, pp 75–92 | Cite as

Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type Lévy Processes

  • Semere HabtemicaelEmail author
  • Musie Ghebremichael
  • Indranil SenGupta


The main goal of this paper is to model variance and volatility swap using superposition of Barndorff-Nielsen and Shephard (BN-S) type models. In particular, in this paper we propose superposition of Lévy process driven by Γ(ν,α) and Inverse Gaussian distributions. Model performance is assessed on data not used to build the model (i.e., test data). It is shown that the prediction error rate for the models considered in this paper are much lower compared to those from previous related models. Moreover, it is shown that unlike previous related models which are restricted to stable markets, the present approach can be applied to both stable and unstable markets.

Keywords and phrases.

Swap Cumulants Stochastic volatility Ornstein-Uhlenbeck process Superposition Cross validation 

AMS (2000) subject classification.

Primary 60G10, 60G51 Secondary 91G70, 91G80 


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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

© Indian Statistical Institute 2017

Authors and Affiliations

  • Semere Habtemicael
    • 1
    Email author
  • Musie Ghebremichael
    • 2
    • 3
  • Indranil SenGupta
    • 4
  1. 1.Department of Applied MathematicsWentworth Institute of TechnologyBostonUSA
  2. 2.Harvard Medical SchoolBostonUSA
  3. 3.Ragon Institute of MGH, MIT, HarvardCambridgeUSA
  4. 4.Department of MathematicsNorth Dakota State UniversityFargoUSA

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