Stochastic Knothe-Rosenblatt: Light-speed Calibration of Stochastic Local Volatility Models

2026-09-30

AI Summary

This study addresses the challenge of intertemporally coupled calibration of risk-neutral marginal distributions in stochastic local volatility (SLV) models by proposing a modular calibration overlay framework. Methodologically, an adaptive Knothe–Rosenblatt transport is introduced to recursively construct a martingale process that matches all marginals while remaining closest to a reference dynamics. Efficient numerical computation is achieved through the Martingale Sinkhorn algorithm combined with Bass martingale construction theory. This framework enables rapid calibration across discrete maturities and guarantees convergence toward continuous-time SLV models. Extensive experiments conducted on Heston, Bergomi, and multi-asset path-dependent models demonstrate its superior computational efficiency and accuracy.

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.

Problem

• Stochastic Local Volatility
• Calibration
• Martingale
• Marginal distributions
• Option smiles

Innovation

• Stochastic Local Volatility
• Knothe-Rosenblatt transport
• Martingale Sinkhorn algorithm
• Bass martingale
• Modular calibration