Paper: arXiv 2406.09959

Abstract

We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically computationally challenging due to the martingale constraint, however, by extending the state space we can identify them with problems that exhibit a certain sequential martingale structure. Our method exploits such structures in combination with entropic regularisation, enabling fast computation of optimal solutions and allowing us to solve problems with a large number of marginals. We demonstrate the method by using it for computing robust price bounds for different options, such as lookback options and Asian options.

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is highly mathematical, featuring extensive derivations on martingale optimal transport theory, duality, and entropic regularization, placing it in the Lab Rrats quadrant. The empirical rigor is limited, as the summary only mentions applying the method to compute price bounds without detailing implementation details, backtest performance, or data processing.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Efficiently compute robust option price bounds<br>via multi-marginal martingale optimal transport"] --> B["Methodology: Sequential Structure +<br>Entropic Regularization"]
  B --> C["Data/Inputs<br>Observed option prices /<br>market marginals"]
  C --> D["Computational Process<br>Convex Optimization via Sinkhorn algorithm"]
  D --> E["Key Outcomes<br>1. Fast computation of optimal martingales<br>2. Robust price bounds for Lookback & Asian options"]