Abstract
Many processes have been proposed over the last 30 years in order to capture the observed stylized facts and in particular the heteroscedasticity and fat tails. The starting point is always the normal random walk written by Bachelier in 1900, and the structure of the extensions can be classified along some broad categories. A first “grand tour” of the various mathematical structures is given in this chapter, presenting the core ideas underlying the ARCH processes, the stochastic volatility processes, and the regime switching processes. The subsequent specific chapters present in detail the basic equation for the price random walk and the most interesting processes for the volatility in each category.
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Zumbach, G. (2013). Process Overview. In: Discrete Time Series, Processes, and Applications in Finance. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31742-2_5
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DOI: https://doi.org/10.1007/978-3-642-31742-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31741-5
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