Paper: arXiv 2609.39256

Authors: Mathias Beiglböck, Manuel Hasenbichler, Gudmund Pammer

Abstract

European option smiles determine the risk-neutral marginal laws of an asset, but not their intertemporal coupling, which is decisive for many applications. The Bass martingale construction selects, among all calibrated martingales, the one closest to Bachelier dynamics; it permits fast calibration at discrete maturities and recovers the Dupire local-volatility (LV) model as the maturity grid is refined. This article develops a modular calibration overlay for existing stochastic and path-dependent volatility models. We recursively construct a martingale that matches all prescribed marginals exactly while remaining as close as possible, in an adapted Knothe-Rosenblatt sense, to the reference dynamics. As with the Bass LV model, each calibration step is amenable to an efficient Martingale Sinkhorn algorithm. We develop the theoretical foundations, numerical implementation and consider convergence to the SLV model. We also benchmark the method for Heston and Bergomi finite-factor path-dependent volatility dynamics and develop the multi-asset extension.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical and novel approach to calibrating stochastic local volatility models, building on advanced concepts like optimal transport and martingale Sinkhorn algorithms. While strong on theoretical foundations and numerical implementation, the empirical rigor is demonstrated through benchmarking rather than extensive backtesting. The modular design and multi-asset extension enhance its practical applicability.

Research Flowchart

  flowchart TD
    A[Research Goal/Question: Calibrate SLV Models Efficiently] --> B{Key Methodology: Stochastic Knothe-Rosenblatt}
    B --> C[Inputs: European Option Smiles, Existing SLV/Path-Dependent Volatility Models (Heston, Bergomi)]
    C --> D{Computational Process: Recursive Martingale Construction & Martingale Sinkhorn Algorithm}
    D --> E[Outcomes: Fast Calibration, Exact Marginal Matching, Convergence to SLV, Multi-asset Extension]