Stochastic Volatility Processes

Gilles Zumbach
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Gilles Zumbach: Consulting in Financial Research

Chapter Chapter 8 in Discrete Time Series, Processes, and Applications in Finance, 2013, pp 129-141 from Springer

Abstract: Abstract In a stochastic volatility process, the positivity and mean reversion of the volatility should be enforced. The mean reversion can be achieved by the drift, equivalent to an Ornstein–Uhlenbeck process. The positivity can be enforced either by an exponential or by taming down the stochastic term by the volatility as done in the Heston process. Both classes of processes are investigated, in the simpler one time scale version, and in a multiscale generalization. Both structures lead to similar mug shots, with an exponential memory or a long-term memory. Yet, all of them are time-reversal invariant, in disagreement with the stylized facts.

Keywords: Option Price; Stochastic Volatility; Stochastic Volatility Model; Time Reversal Symmetry; Multiple Time Scale (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-31742-2_8

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DOI: 10.1007/978-3-642-31742-2_8

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