Deep Bayesian Estimation of the Rough Path-Dependent Volatility Model for Forecasting Purposes

The rough path-dependent volatility (RPDV) model (Parent 2022) effectively captures key empirical features that are characteristic of volatility dynamics, making it a suitable choice for volatility forecasting. However, its complex structure presents challenges when it comes to estimating the model using standard approaches. Taking this into consideration, the objective of this paper is twofold: to develop an estimator function for the RPDV model using historical data, second, to make the RPDV model a competitive tool for volatility forecasting.To achieve this objective, the article proposes an innovative estimation method in which the estimator function is formulated as a deep neural network (DNN) and is trained through interaction with a second DNN. After formalizing the estimation problem within the framework of Bayesian decision theory, the article details the methodology for constructing the estimator function. Finally, a comprehensive evaluation of the obtained estimator is conducted using both synthetic and market data to assess its performance