Arbitrage-Free Implied Volatility Surface Reconstruction via Additive Martingales

By Haochen Luo, Sifan Lin, Xiaolong Luo, An Binh Minh, Yuan Zhang, Chen Liu

Rating

1815
Battle Count: 50

Relevance

9/10
Highly relevant for derivatives trading desks requiring accurate, arbitrage-free IV surfaces for pricing illiquid strikes, hedging, and calculating tail-risk measures like VaR and CVaR. The method offers a significant advantage by guaranteeing no-arbitrage by construction.

Implementation Complexity

7/10
The architecture involves a Transformer-based set encoder and a complex parameter-free decoder using full-support linear convolution and exponential normalization. Training requires careful handling of implicit differentiation for the Black-Scholes inversion. The mathematical foundation (additive martingales) is non-trivial.

Reproducibility

3/5
The paper provides detailed architectural specifications, training protocols, and evaluation metrics. However, the data (OPRA option quotes) is proprietary and obtained from a commercial provider, and no public code repository URL is explicitly provided in the text.

Abstract

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.

Links

arXiv:2610.25671 ยท Paper rankings

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