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

Autor:	Mathieu Rosenbaum, Paul Jusselin
Rok vydání:	2020
Předmět:	Hurst exponent Economics and Econometrics 050208 finance Applied Mathematics 05 social sciences Volterra equations 01 natural sciences Power law 010104 statistics & probability Accounting 0502 economics and business Econometrics Economics Exponent Arbitrage 0101 mathematics Volatility (finance) Market impact Social Sciences (miscellaneous) Finance
Zdroj:	Mathematical Finance
ISSN:	1467-9965 0960-1627
DOI:	10.1111/mafi.12254
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ffb81a308b134fce87299f97236a079b https://doi.org/10.1111/mafi.12254 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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