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SUMMARY:Moment explosions and long-term behaviour of affine stochastic vol
 atility models - Martin Keller-Ressel (TU Vienna)
DTSTART:20080618T131500Z
DTEND:20080618T140000Z
UID:TALK12433@talks.cam.ac.uk
CONTACT:Norros I.
DESCRIPTION:We consider a class of asset pricing models\, where the risk-n
 eutral joint process of log-price and its stochastic variance is given by 
 an affine process in the sense of Duffie\, Filipovic\, and Schachermayer. 
 First we obtain conditions for the price process to be conservative and a 
 martingale. Then we present results on the long-term behavior of the model
 \, including an expression for the invariant distribution of the stochasti
 c variance process. We study moment explosions of the price process\, and 
 provide explicit expressions for the time at which a moment of given order
  becomes infinite. We discuss applications of these results\, in particula
 r to the asymptotics of the implied volatility smile\, and conclude with s
 ome explicit calculations for the Heston model without and with added jump
 s\, a model of Bates and the Barndorff-Nielsen-Shephard model. 
LOCATION:MR14\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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