Chaptergreen2008

Time Change, Volatility, and Turbulence

Ole Eiler Barndorff-Nielsen · Jürgen Schmiegel

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Complex Systems and Time Series Analysis

Abstract

A concept of volatility modulated Volterra processes is introduced. Apart from some brief discussion of generalities, the paper focusses on the special case of backward moving average processes driven by Brownian motion. In this framework, a review is given of some recent modelling of turbulent velocities and associated questions of time change and universality. A discussion of similarities and differences to the dynamics of financial price processes is included.

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References

2003Financial Modelling with Jump Processes 2001The distribution of realized stock return volatility 2004Power and Bipower Variation with Stochastic Volatility and Jumps 2001Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics 1997Processes of normal inverse Gaussian type 1997Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling 2011Quantitative Risk Management 1996Turbulent cascades in foreign exchange markets

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