From microscopic price dynamics to multidimensional rough volatility models

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