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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: Moment explosions and long-term properties of affine stochastic volatility models

Workshop: Concluding Workshop

Time: Tue, December 02, 2008, 10:45-11:15

Speaker: Martin Keller-Ressel

Abstract

We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the
sense of Duffie, Filipovic, and Schachermayer [2003]. We present results on the long-term behavior of the model, including an expression for the stationary distribution of the stochastic variance process. We also study
moment explosions of the price process, and provide explicit expressions for the
first time a moment of given order explodes. We discuss applications to the asymptotics of the implied volatility smile, which are valid e.g. in the Heston model with
and without additional jumps, a model of Bates and the Barndorff-Nielsen-
Shephard model.

Presentation slides (pdf, 299 KB)

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