No-Arbitrage Implies Power-Law Market Impact and Rough Volatility

35 Pages Posted: 6 Jun 2018

See all articles by Paul Jusselin

Paul Jusselin

Ecole Polytechnique, Palaiseau

Mathieu Rosenbaum

Ecole Polytechnique, Palaiseau

Date Written: May 18, 2018

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.

Keywords: No-arbitrage property, market impact, rough volatility, rough Heston model, hyper-rough Heston model, Hawkes processes

JEL Classification: G10

Suggested Citation

Jusselin, Paul and Rosenbaum, Mathieu, No-Arbitrage Implies Power-Law Market Impact and Rough Volatility (May 18, 2018). Available at SSRN: https://ssrn.com/abstract=3180582 or http://dx.doi.org/10.2139/ssrn.3180582

Paul Jusselin

Ecole Polytechnique, Palaiseau ( email )

Palaiseau
France

Mathieu Rosenbaum (Contact Author)

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

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