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.

Keywords: Rough Bergomi Model, Wasserstein Calibration, Monte Carlo Simulation, Volatility Modelling, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents a sophisticated, non-Markovian model (rBergomi) with advanced mathematical techniques like fractional Brownian motion and Wasserstein distance optimization, requiring a high math score. It includes explicit numerical validation and an open-source GitHub repository, indicating strong empirical implementation and data-driven results, warranting a high rigor score.

  flowchart TD
    A["Research Goal<br/>Efficient Calibration in rBergomi"] --> B["Methodology Step 1<br/>Modified Sum-of-Exponentials mSOE Scheme"]
    A --> C["Methodology Step 2<br/>Wasserstein Calibration via Distribution Matching"]
    B --> D["Computational Process<br/>Hybrid Monte Carlo Simulation<br/>Exact Singular Kernel + Multi-Factor Approximation"]
    C --> E["Computational Process<br/>Minimax Optimization<br/>Minimizing Pricing Errors via Lipschitz Payoffs"]
    D --> F["Key Outcomes"]
    E --> F
    F --> G["High Accuracy Pricing<br/>O(n) Cost, especially OTM Options"]
    F --> H["Robust Calibration<br/>Reliable Parameter ID & Path-Dependent Option Generalization"]