The Annals of Applied Probability

The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models

Thorsten Rheinländer and Gallus Steiger

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Abstract

We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have treated either the geometric Lévy case or continuous price processes with an orthogonal volatility process. We proceed by linking the entropy measure to a certain semi-linear integro-PDE for which we prove the existence of a classical solution.

Article information

Source
Ann. Appl. Probab. Volume 16, Number 3 (2006), 1319-1351.

Dates
First available: 2 October 2006

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1159804983

Digital Object Identifier
doi:10.1214/105051606000000240

Mathematical Reviews number (MathSciNet)
MR2260065

Zentralblatt MATH identifier
1154.28305

Subjects
Primary: 28D20: Entropy and other invariants 60G48: Generalizations of martingales 60H05: Stochastic integrals 91B28

Keywords
Relative entropy martingale measures stochastic volatility

Citation

Rheinländer, Thorsten; Steiger, Gallus. The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models. The Annals of Applied Probability 16 (2006), no. 3, 1319--1351. doi:10.1214/105051606000000240. http://projecteuclid.org/euclid.aoap/1159804983.


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