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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps

Workshop: Concluding Workshop

Time: Wed, December 03, 2008, 11:15-11:45

Speaker: Carlo Sgarra

Abstract

We discuss the Esscher martingale transform for exponential processes,
the Esscher martingale transform for linear processes, the minimal martingale
measure, the class of structure preserving martingale measures, and the minimum
entropy martingale measure for stochastic volatility models of
Ornstein-Uhlenbeck type as introduced by Barndorff-Nielsen and Shephard. We show
that in the model with leverage, with jumps both in the volatility and in the
returns, all those measures are different, whereas in the model without
leverage, with jumps in the volatility only and a continuous return process,
several measures coincide, some simplifications can be made and the results are
more explicit.We illustrate our results with parametric examples used in the
literature.

(Presentation based on a joint work with Friedrich Hubalek, Technical University
of Vienna)

Presentation slides (pdf, 134 KB)

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