Rough Martingale Optimal Transport: Finite Pricing Bounds for Non-Modelable Risk Factors under Sparse Data

01 ABSTRACT

Classical Martingale Optimal Transport produces infinite audit bounds for non-modelable risk factors due to sparse market data, and this paper proposes a Rough Martingale Optimal Transport framework that regularizes the transport plan with a rough volatility prior. The authors claim this yields finite, explicit, and asymptotically tight extrapolation bounds, and on SPY and QQQ options they observe stretched exponential tail decay consistent with rough volatility asymptotics. They report validation on live SPX/NDX data and scaling to 30 assets, with roughly $880M in capital relief per $1B exotic book versus classical methods. These identifiability results, calibration observations, and capital relief figures are author claims awaiting independent replication and regulatory verification.

02 KEY FINDINGS

1. The framework regularizes the transport plan with a rough volatility prior, turning the infinite audit bounds of classical MOT into finite, explicit, and asymptotically tight extrapolation bounds, and establishes an identifiability theorem for rough volatility parameters under sparse data, proving that 50 strikes suffice to estimate the Hurst exponent within ±0.05.
2. For the multi-asset case, it proves that the correlation matrix is locally identifiable from marginal option surfaces provided the Hurst exponents are distinct.
3. Calibration on SPY and QQQ options (2019–2024) finds stretched exponential tail decay consistent with rough volatility asymptotics, whereas classical MOT yields trivial bounds; the authors validate on live SPX/NDX data and scale to 30 assets using block-sparse optimization.