Finance and Stochastics

, Volume 22, Issue 2, pp 241–280 | Cite as

The microstructural foundations of leverage effect and rough volatility

  • Omar El Euch
  • Masaaki Fukasawa
  • Mathieu Rosenbaum
Article
  • 66 Downloads

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 

Mathematics Subject Classification (2010)

60F17 60G55 91G70 

JEL Classification

C58 G10 G14 

Notes

Acknowledgements

We thank Neil Shephard for inspiring discussions and Jim Gatheral and Kasper Larsen for very relevant comments. Omar El Euch and Mathieu Rosenbaum gratefully acknowledge the financial support of the ERC Grant 679836 Staqamof and the Chair Analytics and Models for Regulation.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Omar El Euch
    • 1
  • Masaaki Fukasawa
    • 2
  • Mathieu Rosenbaum
    • 1
  1. 1.CMAPÉcole PolytechniquePalaiseau CedexFrance
  2. 2.Graduate School of Engineering ScienceOsaka UniversityToyonaka, OsakaJapan

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