Finance and Stochastics

, Volume 9, Issue 4, pp 563–575

The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps

Article

DOI: 10.1007/s00780-005-0161-z

Cite this article as:
Benth, F.E. & Meyer-Brandis, T. Finance Stochast. (2005) 9: 563. doi:10.1007/s00780-005-0161-z

Abstract.

We derive the density process of the minimal entropy martingale measure in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard [2]. The density is represented by the logarithm of the value function for an investor with exponential utility and no claim issued, and a Feynman-Kac representation of this function is provided. The dynamics of the processes determining the price and volatility are explicitly given under the minimal entropy martingale measure, and we derive a Black & Scholes equation with integral term for the price dynamics of derivatives. It turns out that the minimal entropy price of a derivative is given by the solution of a coupled system of two integro-partial differential equations.

Keywords:

Stochastic volatility Lévy processes subordinators minimal entropy martingale measure density process incomplete market indifference pricing of derivatives integro-partial differential equations 

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Mathematics, University of OsloCentre of Mathematics for ApplicationsOsloNorway
  2. 2.Department of Economics and Business AdministrationAgder University CollegeKristiansandNorway
  3. 3.Department of Mathematics, University of OsloCentre of Mathematics for ApplicationsOsloNorway

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