The 2014 paper Volatility is Rough argues that empirically, fractional Brownian motion with $H=0.1$ is a good description of volatility that comes out of high frequency trading.

Since then there has been some quite some work done. What are the open problems? What types of things are people trying to do?

  • $\begingroup$ there is a web portal devoted entirely to this topic in quantitative finance; for a helpful answer at this site you want to formulate a more precise question, one that can be answered in the brief space of the anwer box. $\endgroup$ – Carlo Beenakker Dec 30 '18 at 15:24

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