Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

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

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 a

Holy Grail Math 9 Rigor 6 ·  September 30, 2026

Calibration of the Bass Local Volatility model

The Bass local volatility model introduced by Backhoff-Veraguas, Beiglböck, Huesmann, and Källblad is a Markov model perfectly calibrated to vanilla options at finitely many maturities, that approximates the Dupire local volatility model. Conze and Henry-Labordère show that its calibration can be ac

Lab Rats Math 8.5 Rigor 3 ·  November 24, 2023

The Gradient Flow of the Bass Functional in Martingale Optimal Transport

Given $μ$ and $ν$, probability measures on $\mathbb R^d$ in convex order, a Bass martingale is arguably the most natural martingale starting with law $μ$ and finishing with law $ν$. Indeed, this martingale is obtained by stretching a reference Brownian motion so as to meet the data $μ,ν$. Unless $μ$

Lab Rats Math 9.5 Rigor 1.5 ·  July 26, 2024

Dynamic reinsurance via martingale transport

We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that, under suitable assumptions, the problem admits a tractable solut

Lab Rats Math 8.5 Rigor 2 ·  January 15, 2026

Change of numeraire for weak martingale transport

Change of numeraire is a classical tool in mathematical finance. Campi-Laachir-Martini established its applicability to martingale optimal transport. We note that the results of Campi-Laachir-Martini extend to the case of weak martingale transport. We apply this to shadow couplings, continuous time

Lab Rats Math 8.5 Rigor 2 ·  June 11, 2024

General duality and dual attainment for adapted transport

We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a multimarginal problem incorporating causality constraints. Moreover, we

Lab Rats Math 9.2 Rigor 1.5 ·  January 22, 2024

An extension of martingale transport and stability in robust finance

While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the robust pricing of American options or the construction of shadow couplings necessitate additional information to be incorp

Lab Rats Math 9.2 Rigor 1.5 ·  April 19, 2023

Strassen's theorem for biased convex order

Strassen’s theorem asserts that for given marginal probabilities $μ,ν$ there exists a martingale starting in $μ$ and terminating in $ν$ if and only if $μ,ν$ are in convex order. From a financial perspective, it guarantees the existence of market-consistent martingale pricing measures for arbitrage-f

Lab Rats Math 9.5 Rigor 1 ·  September 16, 2025

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