{"ID":2846935,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00781","arxiv_id":"2511.00781","title":"Robust Hedging of path-dependent options using a min-max algorithm","abstract":"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 $ t_1$, where $0 \u003c t_1 \u003c T$. We propose a model-free approach to construct such a portfolio. The framework is inspired by the \\textit{primal-dual} Martingale Optimal Transport (MOT) problem, which was pioneered by \\cite{beiglbock2013model}. The optimization problem is to determine the portfolio composition that minimizes the expected worst-case hedging error at $t_1$ (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 \\textit{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 \\textit{Black-Scholes} and a \\textit{Merton Jump diffusion} model are presented. We also provide theoretical bounds on the hedging error at $T$, the maturity of the target option.","short_abstract":"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 $ t_1$, where $0 \u003c t_1 \u003c T$. We propose a model-free approach to construct such a portfolio. The framework i...","url_abs":"https://arxiv.org/abs/2511.00781","url_pdf":"https://arxiv.org/pdf/2511.00781v1","authors":"[\"Purba Banerjee\",\"Srikanth Iyer\",\"Shashi Jain\"]","published":"2025-11-02T03:26:27Z","proceeding":"q-fin.MF","tasks":"[\"q-fin.MF\",\"math.OC\",\"math.PR\",\"q-fin.RM\"]","methods":"[\"Diffusion Model\"]","has_code":false}