How High-Frequency Market Microstructure Can Generate Rough Volatility

Summary

This paper connects high-frequency trading behavior with two observed properties of asset prices: the leverage effect, in which returns and volatility are related, and rough volatility, in which volatility exhibits irregular paths. It builds a microscopic price model using Hawkes processes, which represent clusters of dependent market events. The model incorporates market endogeneity, a no-arbitrage condition, asymmetry between buying and selling, and metaorders, or large orders executed in pieces.

The authors show that the first three features lead, in the long run, to behavior described by a Heston stochastic volatility model with a leverage effect. Adding metaorders produces a rough Heston limit, with both leverage and rough volatility. This offers a theoretical explanation for how market microstructure can contribute to familiar volatility dynamics. The result is model-based: the abstract establishes mathematical limiting behavior, but does not describe an empirical test or show how much of observed volatility these mechanisms explain in actual markets.

Key ideas

• The model uses Hawkes processes to represent dependent high-frequency market events.
• Market endogeneity, no-arbitrage, and buying-selling asymmetry generate a Heston-type limit with leverage effect.
• Including metaorders produces a rough Heston limit with rough volatility as well.
• The paper offers a theoretical microstructure explanation rather than an empirical measurement of its contribution.

Tags

# The microstructural foundations of leverage effect and rough volatility


# The microstructural foundations of leverage effect and rough volatility









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.