Efficient Calibration in the rough Bergomi model by Wasserstein distance

2025-11-29

AI Summary

The rough Bergomi (rBergomi) model poses significant challenges for option pricing and calibration due to its non-Markovian structure. To address this, we develop an efficient computational framework comprising two key components: (i) a distribution-matching calibration method based on the Wasserstein distance, integrated with a minimax optimization paradigm to balance pricing errors across maturities and strikes—thereby enhancing generalization and extrapolation capabilities for path-dependent options; and (ii) an improved singular-oscillatory-exponential (mSOE) Monte Carlo algorithm that combines exact kernel simulation with multi-factor approximation, achieving high-fidelity path generation in *O*(*n*) time complexity. Numerical experiments demonstrate that the mSOE scheme exhibits strong convergence properties; the calibration procedure robustly identifies model parameters; and the overall framework significantly improves both fitting accuracy and robustness for volatility derivatives—particularly Asian and floating-strike options—relative to conventional approaches.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Addresses calibration difficulties in the rough Bergomi model
• Proposes a modified Monte Carlo scheme for efficient pricing
• Uses Wasserstein distance for robust distribution-matching calibration

Innovation

• Modified Sum-of-Exponentials Monte Carlo scheme for efficient simulation
• Wasserstein distance used as optimization objective for calibration
• Minimax formulation against Lipschitz payoffs improves robustness