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Rough Volatility and Fractional Brownian Motion Below H One-Half

Article Quant Q&A · Author: user119615
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Summary

The document asks whether fractional Brownian motion with a Hurst parameter below one-half has applications in mathematical finance, given the questioner’s impression that financial examples tend to use larger values. The answer points to rough volatility research, where volatility is described as a rough path and a low Hurst exponent is cited as an approximate empirical characterization.

This connects fractional Brownian motion with low H to modeling volatility dynamics in finance. The response offers a reference to a paper on rough volatility as a lead, but it does not explain the model, derivation, datasets, or how it might be used in pricing or risk analysis. The cited value is presented in the source as approximate, so it should be read as a reported finding rather than a universal parameter for all markets or periods.

Key ideas

  • Fractional Brownian motion with a Hurst parameter below one-half is linked to rough volatility research.
  • The answer cites an approximate low Hurst exponent for observed volatility.
  • The document points to a research paper but gives no model details or implementation guidance.
  • The cited characterization may not generalize across markets or sample periods.

Tags

VolatilityStatisticsDerivatives pricing
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# Use of fBm when $H<1/2$


# Use of fBm when $H<1/2$












Let H be the Hurst parameter of the Fractional Brownian Motion. Are there any useful areas in mathematical finance where the fractional brownian motion with H<1/2 is used? From all the articles I see they assume that H>1/2. If there are any uses for H<1/2 could you please point me in their direction?

## Answer by steven (score 2)

https://quant.stackexchange.com/a/35749

Recently, some guys have found the volatility is rough path, with $H\approx0.1$. Please see the important paper "Volatility is rough"

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