The discussion into models, inference, options and realized volatility. The SV literature has grown rather organically, with a variety of papers playing important roles for particular branches of the literature.
This reflects the multidisciplinary nature of the research on this topic and has made my task of selecting the papers particularly difficult. Inevitably my selection of articles to appear in this book has been highly subjective. I hope that the authors of the many interesting papers on this topic which I have not included will forgive my choice.
The outline of this Chapter is as follows. In section 2 I will trace the origins of SV and provide links with the basic models used today in the literature. In section 3 I will briefly discuss some of the innovations in the second generation of SV models. These include the use of long-memory volatility processes, the introduction of jumps into the price and volatility processes and the use of SV in interest rate models. The section will finish by discussing various multivariate SV models.
In section 4 I will briefly discuss the literature on conducting inference for SV models. In section 5 I will talk about the use of SV to price options. This application was, for around 15 years, the major motivation for the study of SV models as they seemed to provide a natural way to extend the Black–Schools– Merton framework to cover more empirically realistic situations
. In section 6 I will consider the connection of SV with the literature on realized volatility.
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