2025/11/02 by Banerjee, Purba, Srikanth K. Iyer, Iyer, Srikanth +2
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2511.00781
openalex publication_date 2025/11/02 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
We consider an investor who wants to hedge a path-dependent option with maturity T using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity t1, where 0 < t1 < T. We propose a model-free approach to construct such a portfolio. The framework is inspired by the primal-dual Martingale Optimal Transport (MOT) problem, which was pioneered by \citebeiglbock2013model. The optimization problem is to determine the portfolio composition that minimizes the expected worst-case hedging error at t1 (that coincides with the maturity of the options that are used in the hedging portfolio). The worst-case scenario corresponds to the distribution that yields the worst possible hedging performance. This formulation leads to a min-max problem. We provide a numerical scheme for solving this problem when a finite number of vanilla option prices are available. Numerical results on the hedging performance of this model-free approach when the option prices are generated using a Black-Scholes and a Merton Jump diffusion model are presented. We also provide theoretical bounds on the hedging error at T, the maturity of the target option.