No-Arbitrage Implies Power-Law Market Impact and Rough Volatility
35 Pages Posted: 6 Jun 2018
Date Written: May 18, 2018
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
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