In this talk, we establish a microstructural foundation of the rough Bergomi model. Specifically, we consider financial market models where orders to buy or sell an asset arrive according to a Poisson process, with order sizes depending on a hidden volatility state that takes into account the entire order history. Consequently, each order has a long-lasting impact on volatility.

We show weak convergence of the price-volatility process to a log-normal rough volatility model on the Skorokhod space of right-continuous functions using a recent C-tightness result for càdlàg processes.
This weak convergence result is complemented by providing explicit weak error rates for the marginal distributions. To obtain these rates, we employ a recently established Clark-Ocone formula for Poisson processes.
Together, these results establish our microstructure model as a viable alternative to classical simulation schemes.

The talk is based on joint work with Paul Hager, Ulrich Horst and Wei Xu.