Stochastic Knothe-Rosenblatt: Light-speed Calibration of Stochastic Local Volatility Models
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 sequentially 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.
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BibTeX
@misc{beiglbock2026stochastic,
title = {{Stochastic Knothe-Rosenblatt: Light-speed Calibration of Stochastic Local Volatility Models}},
author = {Mathias Beiglböck and Manuel Hasenbichler and Gudmund Pammer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39256},
eprint = {2609.39256},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39256},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Stochastic Knothe-Rosenblatt: Light-speed Calibration of Stochastic Local Volatility Models
AU - Mathias Beiglböck
AU - Manuel Hasenbichler
AU - Gudmund Pammer
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.39256
UR - https://arxiv.org/abs/2609.39256
AB - 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 sequentially 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.
ER -