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Rough volatility: evidence from option prices

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  • Giulia Livieri
  • Saad Mouti
  • Andrea Pallavicini
  • Mathieu Rosenbaum

Abstract

It has been recently shown that spot volatilities can be very well modeled by rough stochastic volatility type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than 1/2. This result has been established using high frequency volatility estimations from historical price data. We revisit this finding by studying implied volatility based approximations of the spot volatility. Using at-the-money options on the S&P500 index with short maturity, we are able to confirm that volatility is rough. The Hurst parameter found here, of order 0.3, is slightly larger than that usually obtained from historical data. This is easily explained from a smoothing effect due to the remaining time to maturity of the considered options.

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  • Giulia Livieri & Saad Mouti & Andrea Pallavicini & Mathieu Rosenbaum, 2017. "Rough volatility: evidence from option prices," Papers 1702.02777, arXiv.org.
    • Handle: RePEc:arx:papers:1702.02777
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    References listed on IDEAS

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    1. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," CREATES Research Papers 2015-43, Department of Economics and Business Economics, Aarhus University.
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