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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification:
91B28, 60G51, 60G57
JEL Classification:
D46, D52, G13
We are grateful to Kenneth Hvistendahl Karlsen and Thorsten Rheinländer for interesting and fruitful discussions. Two anonymous referees and an associate editor are thanked for their careful reading of an earlier version of the paper leading to a significant improvement of the presentation
Manuscript received: March 2004; final version received: March 2005
Rights and permissions
About this article
Cite this article
Benth, F.E., Meyer-Brandis, T. The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps. Finance Stochast. 9, 563–575 (2005). https://doi.org/10.1007/s00780-005-0161-z
Issue Date:
DOI: https://doi.org/10.1007/s00780-005-0161-z