Unsupervised Learning-based Calibration Scheme for Rough Volatility Models

Abstract

Existing deep learning-based calibration scheme for rough volatility models predominantly rely on supervised learning frameworks, which incur significant computational costs due to the necessity of generating massive synthetic training datasets. In this work, we propose a novel unsupervised learning-based calibration scheme for rough volatility models that eliminates the data generation bottleneck. Our approach leverages the backward stochastic differential equation (BSDE) representation of the pricing function derived by Bayer et al. \cite{bayer2022pricing}. By treating model parameters as trainable variables, we simultaneously approximate the BSDE solution and optimize the parameters within a unified neural network training process, with the terminal misfit as the loss. We theoretically establish that the mean squared error between the model-implied prices and market data is bounded by the loss function. Furthermore, we prove that the loss can be minimized to an arbitary degree, depending on the model's market fitting capacity and the universal approximation capability of neural networks. Numerical experiments for both simulated and historical S\&P 500 data based on rough Bergomi (rBergomi) model demonstrate the efficiency and accuracy of the proposed scheme.