MOT Pricing

mot-pricing is a compact research-oriented package for robust pricing with martingale optimal transport. The repository combines exact discrete linear-programming solvers, entropy-regularized approximations, reporting utilities, and a gallery of reproducible examples.

Public links:

• PyPI: https://pypi.org/project/mot-pricing/
• TestPyPI: https://test.pypi.org/project/mot-pricing/
• Docs: https://anouarmohamed.github.io/NoteBook/
• Repository: https://github.com/AnouarMohamed/NoteBook

Core Problem

The package studies couplings P satisfying:

• S1 ~ mu1
• S2 ~ mu2
• E[S2 | S1] = S1

and computes extremal values of E_P[payoff(S1, S2)] under this martingale restriction.

In discrete form, the associated optimization problem is a linear program over a coupling matrix Pi = (pi_ij).

Main Components

Exact Optimization

The exact solver computes the discrete benchmark by solving the full martingale OT linear program.

Regularized Approximation

The regularized solver computes entropy-penalized approximations across a grid of eps values and records convergence diagnostics.

Reporting

Each experiment produces figures, structural diagnostics, JSON summaries, and a markdown experiment report.

Gallery

The gallery provides curated examples for cross-example comparison and documentation.

Current Gallery Scope

The shipped gallery currently contains nine examples spanning:

• absolute-spread benchmarks
• call and put spread payoffs
• straddle-type payoffs
• centered systems
• wider second marginals
• a quadratic example with a nearly degenerate interval

The gallery therefore covers several qualitatively different regimes rather than a single canned demonstration.

Documentation Map

• Discrete Formulation
• Research Notes
• Regularization Notes
• Numerical Notes
• Getting Started
• CLI Reference
• Artifact Guide
• Examples
• Gallery Table
• Gallery Casebook
• API Guide
• Upgrade Notes
• Publishing

Typical Uses

• exact discrete MOT bounds for two-step problems
• comparison of regularized approximations against LP benchmarks
• payoff sensitivity studies under fixed marginals
• generation of figures and summaries for notes or reports
• structured experimentation with small martingale systems

Suggested Starting Point

1. Getting Started
2. CLI Reference
3. Artifact Guide
4. Examples
5. Gallery Casebook
6. Numerical Notes

This sequence moves from execution to inspection to interpretation.