Computation of the Super-Hedging Strategies for Vanilla Options with Transaction Costs

Emmanuel Lepinette () and Amal Omrani ()
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Emmanuel Lepinette: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Amal Omrani: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres

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Abstract: We study the discrete-time super-hedging problem of European claims under proportional transaction costs in a financial market with one risky asset. For any time t, given the super-hedging price p t , we characterize the corresponding set Γ t (p t ) of super-hedging strategies. Specifically, for a broad class of convex payoff functions and deterministic conditional supports of the relative prices, we prove that Γ t (p t ) forms an explicit closed interval [ϕ l t (p t ), ϕ u t (p t )], which may reduce to a singleton at the minimal price. Numerical and empirical experiments on S&P 500 data illustrate the effectiveness of the method.

Keywords: Super-hedging strategies; Proportional transaction costs; Discrete-time financial markets; No-arbitrage condition; Conditional support (search for similar items in EconPapers)
Date: 2026-05-19
Note: View the original document on HAL open archive server: https://hal.science/hal-05626560v1
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