So far, path-dependent volatility models have drawn little attention from both practitioners and academics compared to local volatility and stochastic volatility models. This is unfair: in this article we show that they combine benefits from both. Like the local volatility model, they are...

This article introduces the rough path-dependent volatility (RPDV) model, a model structurally adapted to jointly capture two major empirical features of volatility: its rough behavior and its path-dependence.After presenting it in its general form and its link with other existing models in the...

We learn from data that volatility is mostly path-dependent: at least 85-90% of the variance of the implied volatility of equity indexes is explained endogenously by past index returns, and around 60% for (noisy estimates of) future daily realized volatility. The path-dependency that we uncover...