ORIGINAL ARTICLE
No-arbitrage implies power-law market impact and rough volatility
Paul Jusselin,
Mathieu Rosenbaum,
Paul Jusselin
École Polytechnique, CMAP, Palaiseau Cedex, France
Search for more papers by this authorCorresponding Author
Mathieu Rosenbaum
École Polytechnique, CMAP, Palaiseau Cedex, France
Correspondence
Mathieu Rosenbaum, École Polytechnique, CMAP, Route de Saclay, 91128 Palaiseau Cedex, France.
Email: mathieu.rosenbaum@polytechnique.edu
Search for more papers by this authorPaul Jusselin,
Mathieu Rosenbaum,
Paul Jusselin
École Polytechnique, CMAP, Palaiseau Cedex, France
Search for more papers by this authorCorresponding Author
Mathieu Rosenbaum
École Polytechnique, CMAP, Palaiseau Cedex, France
Correspondence
Mathieu Rosenbaum, École Polytechnique, CMAP, Route de Saclay, 91128 Palaiseau Cedex, France.
Email: mathieu.rosenbaum@polytechnique.edu
Search for more papers by this authorFunding information:
ERC Grant 679836 Staqamof and Chair Analytics and Models for Regulation.
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 in a quite general framework, under no-arbitrage assumption, the market impact function can only be of power-law type. Furthermore, we prove 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.
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