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The microstructural foundations of leverage effect and rough volatility

Omar Euch (), Masaaki Fukasawa () and Mathieu Rosenbaum ()
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Omar Euch: École Polytechnique
Masaaki Fukasawa: Osaka University
Mathieu Rosenbaum: École Polytechnique

Finance and Stochastics, 2018, vol. 22, issue 2, 241-280

Abstract: Abstract We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in this model some of the main features of market microstructure in the context of high frequency trading: high degree of endogeneity of market, no-arbitrage property, buying/selling asymmetry and presence of metaorders. We prove that when the first three of these stylized facts are considered within the framework of our microscopic model, it behaves in the long run as a Heston stochastic volatility model, where a leverage effect is generated. Adding the last property enables us to obtain a rough Heston model in the limit, exhibiting both leverage effect and rough volatility. Hence we show that at least part of the foundations of leverage effect and rough volatility can be found in the microstructure of the asset.

Keywords: Market microstructure; High frequency trading; Leverage effect; Rough volatility; Hawkes processes; Limit theorems; Heston model; Rough Heston model; 60F17; 60G55; 91G70 (search for similar items in EconPapers)
JEL-codes: C58 G10 G14 (search for similar items in EconPapers)
Date: 2018
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