Paper: arXiv 2603.24605

Authors: Bryan Liang, Marcel Nutz, Shunan Sheng, Valentin Tissot-Daguette

Abstract

Martingale Optimal Transport (MOT) provides a framework for robust pricing and hedging of illiquid derivatives. Classical MOT enforces exact calibration of model marginals to the mid-prices of vanilla options. Motivated by the industry practice of fitting bid and ask marginals to vanilla prices, we introduce a relaxation of MOT in which model-implied volatilities are only required to lie within observed bid–ask spreads; equivalently, model marginals lie between the bid and ask marginals in convex order. The resulting Bid–Ask MOT (BAMOT) yields realistic price bounds for illiquid derivatives and, via strong duality, can be interpreted as the superhedging price when short and long positions in vanilla options are priced at the bid and ask, respectively. We further establish convergence of BAMOT to classical MOT as bid–ask spreads vanish, and quantify the convergence rate using a novel distance intrinsically linked to bid–ask spreads. Finally, we support our findings with several synthetic and real-data examples.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically sophisticated relaxation of Martingale Optimal Transport (MOT) by incorporating real-world bid-ask spreads via convex ordering. It balances rigorous theoretical duality proofs with practical empirical demonstrations on synthetic and real market data.

Research Flowchart

  flowchart TD
    A[Goal: Robust derivative pricing & superhedging incorporating bid-ask spreads] --> B[Input: Market Vanilla Option Bid-Ask Spreads & Marginals]
    B --> C[Method: Bid-Ask Martingale Optimal Transport - BAMOT]
    C --> D[Constraint Setup: Model marginals bounded between bid & ask in convex order]
    D --> E[Duality Analysis & Convergence Proofs]
    E --> F[Validation: Synthetic & Real-Data Numerical Experiments]
    F --> G[Outcomes: Realistic price bounds, superhedging strategies & convergence to classical MOT]

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2 of 52 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.