Efficient Calibration in the rough Bergomi model by Wasserstein distance

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.