We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently used to solve efficiently (martingale) optimal transport problems.
@article{arxiv.1902.04456,
title = {Building arbitrage-free implied volatility: Sinkhorn's algorithm and variants},
author = {Hadrien De March and Pierre Henry-Labordere},
journal= {arXiv preprint arXiv:1902.04456},
year = {2023}
}