Paper: arXiv 2512.00448

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (41)

  1. Strong convergence rates for M arkovian representations of fractional B rownian motion (2019) — link
  2. Markovian approximation of the rough B ergomi model for M onte C arlo option pricing (2021)
  3. Deep calibration with random grids — → 2306.11061
  4. Pricing under rough volatility (2016)
  5. Volatility is rough (2022)
  6. Markovian approximations of stochastic Volterra equations with the fractional kernel (2023)
  7. On VIX futures in the rough B ergomi model (2018)
  8. A pproximation of 1/x by exponential sums in [1,$\infty$) (2005)
and 33 more
  1. Neural SDEs as infinite-dimensional GANs (2021)
  2. Neural options pricing (2021)
  3. Hybrid scheme for Brownian semistationary processes (2017)
  4. Fractional Brownian motion and the Markov property (1998)
  5. Fractional Brownian motions, fractional noises and applications (1968)
  6. Learning fractional white noises in neural stochastic differential equations (2022)
  7. Multifactor approximation of rough volatility models (2019)
  8. Nonlinear approximation theory (2012)
  9. Hybrid multifactor scheme for stochastic V olterra equations with completely monotone kernels (2022)
  10. Topics in optimal transportation (2021)
  11. Adam: A Method for Stochastic Optimization (2015)
  12. Completely monotonic functions (2001)
  13. Weak M arkovian approximations of rough H eston — → 2309.07023
  14. Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models (2021)
  15. Parsimonious modeling of yield curves (1987)
  16. Pathwise versions of the Burkholder–Davis–Gundy inequality (2015)
  17. Markov processes over denumerable products of spaces, describing large systems of automata (1969)
  18. Calculation of the Wasserstein distance between probability distributions on the line (1974)
  19. Why the 1- W asserstein distance is the area between the two marginal CDFs (2021) — link
  20. Risk-neutral densities: A review (2018)
  21. On the martingale property in the rough B ergomi model (2019)
  22. Weak error rates for option pricing under linear rough volatility (2022)
  23. Fast evaluation of the C aputo fractional derivative and its applications to fractional diffusion equations (2017)
  24. A generative adversarial network approach to calibration of local stochastic volatility models (2020)
  25. TensorFlow: a system for Large-Scale machine learning (2016)
  26. Weak error estimates for rough volatility models — → 2212.01591
  27. Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions (2020)
  28. A neural network-based framework for financial model calibration (2019)
  29. Arbitrage-free SVI volatility surfaces (2014)
  30. Gaussian measures (1998)
  31. A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives (2004)
  32. A limited memory algorithm for bound constrained optimization (1995)
  33. Algorithm 778: L-BFGS-B : Fortran subroutines for large-scale bound-constrained optimization (1997)

3 of 41 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.