Robust Hedging of path-dependent options using a min-max algorithm

Battle Count: 67

Highly relevant for derivatives desks and risk management teams. The model-free approach eliminates model risk in hedging, which is critical for exotic option portfolios. The min-max formulation provides guaranteed worst-case error bounds. However, practical implementation requires solving LP problems and the approach is limited to static hedging with short-maturity options. The finding that traditional super-hedging does not necessarily yield minimum worst-case error is practically significant.

High complexity due to: (1) construction of discretely supported marginals from finite call prices, (2) formulation and solution of the min-max problem involving nested LP optimization, (3) handling of modified MOT with conditional expectations, (4) numerical stability issues with solver-dependent solutions, (5) need for careful grid selection and convergence verification. Requires expertise in optimal transport theory, linear programming, and numerical optimization.

The paper specifies the use of Gurobi solver for inner maximization and scipy.optimize SLSQP for outer minimization. Parameters for BS and MJD models are provided. However, no code repository is mentioned, and the non-uniform grid construction details and specific solver settings are not fully documented. Solutions may be non-unique depending on solver choice.