Volatility has to be rough
Mathematical Finance
2020-02-24 v1
Abstract
First, we give an asymptotic expansion of short-dated at-the-money implied volatility that refines the preceding works and proves in particular that non-rough volatility models are inconsistent to a power law of volatility skew. Second, we show that given a power law of volatility skew in an option market, a continuous price dynamics of the underlying asset with non-rough volatility admits an arbitrage opportunity. The volatility therefore has to be rough in a viable market of the underlying asset of which the volatility skew obeys a power law.
Cite
@article{arxiv.2002.09215,
title = {Volatility has to be rough},
author = {Masaaki Fukasawa},
journal= {arXiv preprint arXiv:2002.09215},
year = {2020}
}