Work

No‐arbitrage implies power‐law market impact and rough volatility

Year: 2020

Type: article

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.

Source: Mathematical Finance

DOI: 10.1111/mafi.12254

Authors: Paul Jusselin, Mathieu Rosenbaum

Institutions: École Polytechnique, Centre de Mathématiques Appliquées de l'École polytechnique

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, H2020 European Research Council

Awards: LABEX Finance & Croissance Durable, LabEx Mathématique Hadamard, Statistical modelling across price and time scales: a quantitative approach to modern financial regulation