  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 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.
