Volatility is Rough

J. Gatheral,T. Jaisson,M. Rosenbaum

World Scientific Lecture Notes in FinanceOptions — 45 Years since the Publication of the Black–Scholes–Merton Model（2023）

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摘要

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 model the log-volatility as a fractional Brownian motion with H

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volatility

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