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A didactic note on affine stochastic volatility models. (English) Zbl 1104.60024
Kabanov, Yuri (ed.) et al., From stochastic calculus to mathematical finance. The Shiryaev Festschrift. Allmost all papers based on the presentation at the second Bachelier colloquium on stochastic calculus and probability, Meatbief, France, January 9–15, 2005. Berlin: Springer (ISBN 3-540-30782-6/hbk). 343-368 (2006).
Many stochastic volatility models in the literature are based on an affine structure, which makes them handy for analytical calculations. The underlying general class of affine Markov processes has been characterized completely and investigated thoroughly by D. Duffie, D. Filipovic and W. Schachermayer [Ann. Appl. Probab. 13, No. 3, 984–1053 (2003; Zbl 1048.60059)]. In the present note, the author takes a look at this set of processes and, in particular, affine stochastic volatility models from the point of view of semimartingales and time changes. In the course of doing so, the author beautifully explains the intuition behind semimartingale characteristics.
For the entire collection see [Zbl 1087.60004].

MSC:
60G99 Stochastic processes
91B70 Stochastic models in economics
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