# Arbitrage-Free Implied Volatility Surface Reconstruction via Additive Martingales

arXiv: https://arxiv.org/abs/2610.25671 · HTML: https://mlsanity.com/paper/2610.25671/

## Key facts

- No citing papers in the map yet (data through 19 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 19 Oct 2026.

## Placed in

- 3D reconstruction and neural rendering

## Builds on (most cited first, 8 of 8)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Deep Smoothing of the Implied Volatility Surface](https://mlsanity.com/paper/1906.05065/) (2019)
- [Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders](https://mlsanity.com/paper/2108.04941/) (2021)
- [Neural Term Structure of Additive Process for Option Pricing](https://mlsanity.com/paper/2408.01642/) (2024)
- [A Risk-Neutral Neural Operator for Arbitrage-Free SPX-VIX Term Structures](https://mlsanity.com/paper/2511.06451/) (2025)

## Abstract (arXiv)

This work focuses on reconstructing a continuous implied volatility (IV) surface from a small number of option quotes, a fundamental task for option pricing and risk management. We propose Additive Martingale (AddMart), a few-shot IV surface reconstruction framework that satisfies static no-arbitrage conditions by construction. Rather than predicting IVs directly, AddMart maps sparse quotes to non-negative increment densities of an exponential additive martingale, from which valid risk-neutral marginals and IVs are recovered. By incorporating the no-arbitrage structure directly into its architecture, rather than enforcing it through regularization in the learning objective, AddMart produces IV surfaces that satisfy static no-arbitrage conditions throughout the domain. Extensive experiments on ten real-option datasets demonstrate that AddMart achieves competitive reconstruction accuracy with no material static arbitrage violations, while directly enabling the estimation of VaR, CVaR, and crash probabilities.