This paper introduces a novel approach to calibrating rough volatility models by using convolutional neural networks (CNNs) to estimate the Hölder exponent (or Hurst parameter H) from simulated sample paths of the rBergomi model. The authors generate training data via Cholesky decomposition, ensuring exact distribution of the log volatility process, and train a one-dimensional CNN with three convolutional layers, max pooling, dropout, and dense layers. The network is trained on paths of varying lengths (100 to 500) and for different sampling schemes of H: discrete grid, uniform on (0,0.5), and Beta(1,9) distribution. The CNN's performance is compared to the least squares method of Gatheral et al. (2018), which is commonly used in practice.

The results demonstrate that the CNN significantly outperforms the least squares approach in both accuracy and speed. For example, with input length 100 and discretised H, the CNN achieves a root mean square error (RMSE) of 0.0104 compared to 0.2118 for least squares, while training and testing take under 70 seconds versus nearly 600 seconds. The CNN also shows robustness to variations in the parameter η (volatility of volatility) and to random sampling of both η and H, maintaining RMSE around 0.01–0.02. Additionally, the method generalises to fractional Brownian motion paths, confirming its applicability beyond the rBergomi model.

The significance of this work lies in providing a fast, accurate, and robust calibration tool for rough volatility models, which are increasingly important in quantitative finance for capturing the observed roughness of volatility. The CNN approach offers a practical alternative to computationally expensive or less accurate methods, enabling real-time calibration from market data. The paper also opens the door for further applications of deep learning in financial model calibration.