It has been recently shown that spot volatilities can be closely modeled by rough stochastic volatility-type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than half. 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.

Rough volatility: Evidence from option prices

Livieri, Giulia;
2018

Abstract

It has been recently shown that spot volatilities can be closely modeled by rough stochastic volatility-type dynamics. In such models, the log-volatility follows a fractional Brownian motion with Hurst parameter smaller than half. 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.
2018
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Rough volatility, fractional Brownian motion, implied volatility, Medvedev–Scaillet approximation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/83005
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