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      Rough volatility: evidence from option prices

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          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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          Most cited references 5

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          The Pricing of Options and Corporate Liabilities

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            A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

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              The Pricing of Options on Assets with Stochastic Volatilities

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                Author and article information

                Journal
                2017-02-09
                Article
                1702.02777

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                q-fin.ST q-fin.MF

                Statistical finance

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