Paper: arXiv 2610.25671

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

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel approach to IV surface reconstruction using additive martingales, directly embedding no-arbitrage conditions. It demonstrates strong empirical results across multiple datasets, showcasing both theoretical depth and practical applicability. The methodology is well-articulated, though full reproducibility would benefit from explicit code/data availability.

Research Flowchart

  flowchart TD
    A[Research Goal: Reconstruct Arbitrage-Free IV Surface] --> B(Input: Sparse Option Quotes);
    B --> C{Methodology: Additive Martingale (AddMart)};
    C --> D[Computational Process: Map Quotes to Non-negative Increment Densities];
    D --> E(Output: Valid Risk-Neutral Marginals & IVs);
    E --> F[Key Outcome 1: Arbitrage-Free IV Surface by Construction];
    F --> G[Key Outcome 2: Competitive Reconstruction Accuracy & No Arbitrage Violations];
    G --> H[Key Outcome 3: Estimation of VaR, CVaR, Crash Probabilities];