# Building arbitrage-free implied volatility: Sinkhorn's algorithm and variants

## TL;DR

This paper introduces a fast, convergent numerical method using Sinkhorn's algorithm to construct arbitrage-free implied volatility surfaces from market quotes, improving efficiency in financial modeling.

## Contribution

It adapts Sinkhorn's algorithm for arbitrage-free implied volatility surface construction, providing a novel, efficient solution with proven convergence.

## Key findings

- The method efficiently constructs arbitrage-free surfaces from bid-ask quotes.
- The algorithm guarantees convergence to a valid implied volatility surface.
- It offers a practical tool for financial practitioners to model volatility surfaces.

## Abstract

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.