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Lithuanian Mathematical Journal

, Volume 58, Issue 4, pp 408–420 | Cite as

Moments of the asset price for the Barndorff-Nielsen and Shephard model

  • Atif Ihsan
  • Indranil SenGupta
Article
  • 31 Downloads

Abstract

In this paper, we derive closed-form formulas for moments of the asset price in the Barndorff-Nielsen and Shephard (BN–S) stochastic volatility model. We also present similar results where the market is driven by a BN–S-type stochastic process. It is shown that in both cases the results depend on the cumulant transform of the background driving Lévy process for the models. In this paper, we have also obtain various approximate expressions for the expected value of the square-root process for the shifted asset price with respect to the BN–S model.

Keywords

moments Lévy process Barndorff-Nielsen and Shephard model cumulant transform Girsanov’s theorem 

MSC

91G20 91G70 60G51 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNorth Dakota State UniversityFargoUSA

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