Deriving Multidimensional Rough Volatility from High-Frequency Interactions

Summary

This work connects the rough volatility observed in financial assets with the microscopic dynamics linking multiple asset prices. While much prior modeling has focused on a single asset, the authors investigate how multivariate rough volatility models can emerge from interactions at high frequency.

They construct microscopic models using Hawkes processes to represent cross-asset interactions, then study the models’ long-term scaling limits. The analysis examines how momentum and mean reversion at the microscopic level affect multidimensional price formation, and it recovers established features of high-dimensional stock correlation matrices. The document presents a modeling and theoretical analysis rather than a trading strategy or direct empirical performance test; it does not specify assets, estimation procedures, or numerical results in the available summary.

Key ideas

• Hawkes processes model high-frequency interactions among multiple asset prices.
• Long-term scaling limits of these microscopic models can produce multidimensional rough volatility models.
• Microscopic momentum and mean reversion influence how joint prices form.
• The resulting analysis recovers classical properties of high-dimensional stock correlation matrices.

Tags

# From microscopic price dynamics to multidimensional rough volatility models


# From microscopic price dynamics to multidimensional rough volatility models









Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that reproduce accurately high frequency cross-asset interactions and investigate their long term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion on the multidimensional price formation process. We in particular recover classical properties of high-dimensional stock correlation matrices.

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.