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Volatility is rough

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  • Jim Gatheral
  • Thibault Jaisson
  • Mathieu Rosenbaum

Abstract

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H

Suggested Citation

  • Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    • Handle: RePEc:arx:papers:1410.3394
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    References listed on IDEAS

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