Efficient Simulation and Calibration of the Rough Bergomi Model via Wasserstein Distance

Abstract

Despite the empirical success of the rough Bergomi (rBergomi) model in modeling volatility dynamics, its practical use remains challenging due to high computational complexity in both pricing and calibration arising from its non-Markovian structure. To address these difficulties, we develop an efficient computational framework. First, we propose a modified-sum-of-exponentials (mSOE) Monte Carlo scheme within the class of hybrid multifactor approximations. The method combines an exact treatment of the singular kernel over the first time step with a sum-of-exponentials approximation over the remaining time interval, and exact Gaussian simulation of the resulting multifactor components. For a fixed number of exponential terms, the method maintains linear online complexity with respect to the number of time steps. It achieves high pricing accuracy in numerical experiments, particularly for out-of-the-money options. Second, building on this pricing engine, we formulate a calibration approach based on distributional matching of the terminal underlying asset via the Wasserstein-1 distance. Instead of fitting option prices only at selected strikes, this method compares model-generated and market-implied terminal distributions through the Kantorovich-Rubinstein dual representation. Numerical experiments indicate that the mSOE scheme exhibits stable convergence, and the Wasserstein-based calibration scheme improves parameter recovery, optimization stability, and out-of-sample performance relative to conventional MSE-based fitting in the rBergomi setting considered in this paper.