Rough Martingale Optimal Transport: Theory, Implementation, and Regulatory Applications for Non-Modelable Risk Factors

Battle Count: 50

Highly relevant for quantitative trading desks dealing with exotic derivatives, basket options, and regulatory capital optimization. The framework directly addresses FRTB compliance for NMRFs, provides finite pricing bounds for deep OTM options, enables multi-asset correlation recovery from marginals, and offers substantial capital relief (88%). Particularly relevant for banks and trading firms managing large exotic books. The computational scalability (N=30 in 3 minutes) makes it production-ready. However, it is more focused on risk management and regulatory compliance than on alpha generation or trading strategy development.

High complexity due to: (1) Rough Heston calibration requiring fractional Riccati equation solutions and Malliavin calculus for Fisher Information; (2) Multi-asset rough copula construction with block-sparse Newton optimization; (3) Monte Carlo simulation of fractional Brownian motion paths; (4) Large Deviation Principle computations for tail bounds; (5) JAX-based auto-differentiation for gradient computations; (6) Adaptive quadrature for characteristic function evaluation. The paper provides detailed algorithms but implementation requires expertise in stochastic analysis, optimal transport, and numerical methods. The block-sparse structure and Schur complement techniques add significant engineering complexity.

The paper provides detailed algorithms (Algorithm 1-3), specifies hardware (Apple M4 chip), software stack (Python 3.9.6, NumPy, JAX, SciPy), data sources (yfinance/CBOE), and filtering criteria. However, no code repository is linked. The mathematical proofs are provided in appendices. The 100-seed cross-validation and specific parameter settings aid reproducibility, but the full implementation details for the block-sparse Newton method and rough Heston characteristic function computation would require additional code.