Paper: arXiv 2611.17247

Authors: Erhan Bayraktar, Shuoqing Deng, Daxin Huang, Dominykas Norgilas

Abstract

Martingale optimal transport (MOT) provides model-independent bounds for option prices calibrated to vanilla options, assuming frictionless trading in the underlying. In this work, we consider the case where dynamic trading incurs quadratic temporary price impact. First, we prove a duality result for the superhedging price. In particular, the primal of the duality relaxes the strict martingale constraint by penalizing the deviation from a specific martingale. Second, for one asset and one trading period, we interpret this price-impact martingale optimal transport (PIMOT) as a weak optimal transport (WOT) problem, and provide a characterization in the spirit of Wasserstein projection. Finally, we justify that PIMOT is an interpolation between MOT and classical optimal transport (OT), and derive the convergence rate to both sides. Numerical examples with SPX option data show how the price bounds per claim depend on the order size.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework extending Martingale Optimal Transport to include price impact, demonstrating strong theoretical novelty. While numerical examples are provided, the empirical section is not the primary focus, yet it offers sufficient detail for understanding the application.

Research Flowchart

  flowchart TD
    A[Research Goal: Model-independent Option Pricing with Price Impact] --> B{Key Methodology: Price-Impact Martingale Optimal Transport (PIMOT)};
    B --> C{Method Step 1: Duality Result for Superhedging Price};
    B --> D{Method Step 2: PIMOT as Weak Optimal Transport (WOT)};
    C & D --> E[Data/Inputs: SPX Option Data];
    E --> F[Computational Processes: Numerical Examples, Convergence Rate Derivations];
    F --> G[Key Findings: Price Bounds per Claim Depend on Order Size; PIMOT Interpolates MOT & OT];

Cited References (23)

  1. The Fundamental Theorem of Weak Optimal Transport (2025) — link
  2. The McCormick Martingale Optimal Transport — → 2401.15552
  3. Dynamic programming principle and computable prices in financial market models with transaction costs (2023) — link
  4. Weak transport for non‐convex costs and model‐independence in a fixed‐income market (2020) — link
  5. Sampling of probability measures in the convex order by Wasserstein projection (2020) — link
  6. Robust Pricing and Hedging of Options on Multiple Assets and Its Numerics (2019) — link
  7. Existence, duality, and cyclical monotonicity for weak transport costs (2018) — link
  8. On a mixture of Brenier and Strassen Theorems (2018) — link
and 15 more
  1. Robust Utility Maximization in Discrete-Time Markets with Friction (2016) — link
  2. Consistency of option prices under bid–ask spreads (2016) — link
  3. Duality Formulas for Robust Pricing and Hedging in Discrete Time (2016) — link
  4. Hedging with temporary price impact (2015) — link
  5. Kantorovich duality for general transport costs and applications (2014) — link
  6. Dynamic Trading with Predictable Returns and Transaction Costs (2013) — link
  7. OPTION PRICING AND HEDGING WITH EXECUTION COSTS AND MARKET IMPACT (2013) — link
  8. Robust hedging with proportional transaction costs (2013) — link
  9. A Stochastic Control Approach to No-Arbitrage Bounds Given Marginals, with an Application to Lookback Options (2013) — link
  10. Model-independent bounds for option prices—a mass transport approach (2011) — link
  11. Duality and convergence for binomial markets with friction (2011) — link
  12. Local martingales and the fundamental asset pricing theorems in the discrete-time case (1998) — link
  13. Optimal execution for portfolio transactions (2006)
  14. On the existence of probability measures with given marginals (1978) — link
  15. Prices of State-Contingent Claims Implicit in Option Prices (1978) — link

1 of 23 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2570 linked papers.