No-arbitrage implies power-law market impact and rough volatility
Statistical Finance
2018-05-21 v1 Mathematical Finance
Trading and Market Microstructure
Abstract
Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that under no-arbitrage assumption, the market impact function can only be of power-law type. Furthermore, we prove that this implies that the macroscopic price is diffusive with rough volatility, with a one-to-one correspondence between the exponent of the impact function and the Hurst parameter of the volatility. Hence we simply explain the universal rough behavior of the volatility as a consequence of the no-arbitrage property. From a mathematical viewpoint, our study relies in particular on new results about hyper-rough stochastic Volterra equations.
Cite
@article{arxiv.1805.07134,
title = {No-arbitrage implies power-law market impact and rough volatility},
author = {Paul Jusselin and Mathieu Rosenbaum},
journal= {arXiv preprint arXiv:1805.07134},
year = {2018}
}