Rough Bergomi Model

Efficient Calibration in the rough Bergomi model by Wasserstein distance ArXiv ID: 2512.00448 “View on arXiv” Authors: Changqing Teng, Guanglian Li Abstract Despite the empirical success in modeling volatility of the rough Bergomi (rBergomi) model, it suffers from pricing and calibration difficulties stemming from its non-Markovian structure. To address this, we propose a comprehensive computational framework that enhances both simulation and calibration. First, we develop a modified Sum-of-Exponentials (mSOE) Monte Carlo scheme which hybridizes an exact simulation of the singular kernel near the origin with a multi-factor approximation for the remainder. This method achieves high accuracy, particularly for out-of-the-money options, with an $\mathcal{“O”}(n)$ computational cost. Second, based on this efficient pricing engine, we then propose a distribution-matching calibration scheme by using Wasserstein distance as the optimization objective. This leverages a minimax formulation against Lipschitz payoffs, which effectively distributes pricing errors and improving robustness. Our numerical results confirm the mSOE scheme’s convergence and demonstrate that the calibration algorithm reliably identifies model parameters and generalizes well to path-dependent options, which offers a powerful and generic tool for practical model fitting. ...

Unsupervised learning-based calibration scheme for Rough Bergomi model ArXiv ID: 2412.02135 “View on arXiv” Authors: Unknown Abstract Current deep learning-based calibration schemes for rough volatility models are based on the supervised learning framework, which can be costly due to a large amount of training data being generated. In this work, we propose a novel unsupervised learning-based scheme for the rough Bergomi (rBergomi) model which does not require accessing training data. The main idea is to use the backward stochastic differential equation (BSDE) derived in [“Bayer, Qiu and Yao, {“SIAM J. Financial Math.”}, 2022”] and simultaneously learn the BSDE solutions with the model parameters. We establish that the mean squares error between the option prices under the learned model parameters and the historical data is bounded by the loss function. Moreover, the loss can be made arbitrarily small under suitable conditions on the fitting ability of the rBergomi model to the market and the universal approximation capability of neural networks. Numerical experiments for both simulated and historical data confirm the efficiency of scheme. ...