Backward Hedging for American Options with Transaction Costs

Ludovic Goudenège (goudenege@math.cnrs.fr), Andrea Molent and Antonino Zanette
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Ludovic Goudenège: INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
Andrea Molent: Università degli Studi di Udine - University of Udine [Italie]
Antonino Zanette: Università degli Studi di Udine - University of Udine [Italie]

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Abstract: In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which is based on either a risk measure or the mean squared error of the hedging strategy at maturity. The proposed algorithm moves backward in time, determining, for each time-step and different market states, the optimal hedging strategy that minimizes the loss function at the time the option is exercised, by assuming that the strategy used in the future for hedging the liability is the one determined at the previous steps of the algorithm. The approach avoids machine learning and instead relies on classic optimization techniques, Monte Carlo simulations, and interpolations on a grid. Comparisons with the Deep Hedging algorithm in various numerical experiments showcase the efficiency and accuracy of the proposed method.

Keywords: Hedging; Greeks; Transaction costs; American options; Heston model (search for similar items in EconPapers)
Date: 2023-05-10
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04308637

DOI: 10.48550/arXiv.2305.06805

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