The Rough Path-Dependent Volatility Model
Résumé
This paper introduces the rough path-dependent volatility (RPDV) model, which is structurally adapted to jointly capturing two major empirical features of volatility, namely its rough behavior and path-dependence. After presenting the model in its general form and its link with other existing models in the literature, we then present a Markovian multi-factor approximation of the RPDV model based on the work of Abi Jaber (2019). Finally, the paper focuses on a selection of RPDV model specifications that are interpretable from an economic point of view, leading to the formulation of different hypotheses about both asset price and volatility formation mechanisms.