Rough Volatility: Evidence from Option Prices

18 Pages Posted: 10 Feb 2017

See all articles by Giulia Livieri

Giulia Livieri

Scuola Normale Superiore

Saad Mouti

Université Paris VI Pierre et Marie Curie

Andrea Pallavicini

Intesa Sanpaolo

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau

Date Written: February 9, 2017

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.

Keywords: Rough Volatility, Fractional Brownian Motion, Implied Volatility, Medvedev-Scaillet Approximation

JEL Classification: C00

Suggested Citation

Livieri, Giulia and Mouti, Saad and Pallavicini, Andrea and Rosenbaum, Mathieu, Rough Volatility: Evidence from Option Prices (February 9, 2017). Available at SSRN: https://ssrn.com/abstract=2914086 or http://dx.doi.org/10.2139/ssrn.2914086

Giulia Livieri (Contact Author)

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Saad Mouti

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013
France

Andrea Pallavicini

Intesa Sanpaolo ( email )

Largo Mattioli 3
Milan, MI 20121
Italy

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

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