This article introduces the factorial path-dependent market (FPDM) model, a multivariate asset price dynamics model in which these dynamics are determined by a set of elementary factors. In this framework, both the factorial drift and factorial volatilities are conditioned by the past dynamics of the factorial portfolios, resulting in a model mostly path-dependent. Derived from this theoretical foundation, the paper subsequently designs a market generator positioned midway between parametric models based on strong assumptions and purely data-driven approaches. The aim is to combine the best of both worlds, offering a model capable of faithfully reproducing the empirical financial dynamics while maintaining a clear understanding of the financial phenomena driven by the simulated price paths. To evaluate the effectiveness of the proposed approach, a thorough out-of-sample assessment of the market generator is conducted based on the S&P500 investment universe.