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

By Paul Jusselin, Mathieu Rosenbaum. Mathematical Finance, 2018

61 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/c6f14bed40ffc5612d5c973a3b498e51d421948a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (2020, methodology): “This model arises as limit of natural Hawkes process-based models of price and order flow, see [12, 27, 28].”