有交易成本的美式期权后向套期保值

IF 1.4 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Decisions in Economics and Finance Pub Date : 2024-08-06 DOI:10.1007/s10203-024-00472-y
Ludovic Goudenège, Andrea Molent, Antonino Zanette
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引用次数: 0

摘要

在本文中,我们介绍了一种名为 "后向对冲"(Backward Hedging)的算法,旨在对冲欧式和美式期权,同时考虑交易成本。最优策略通过最小化适当的损失函数来确定,该函数基于风险度量或到期时对冲策略的均方误差。具体地说,该算法在时间上向后移动,在每个时间步和不同的市场状态下,通过假设未来用于对冲负债的策略是算法前几步所确定的策略,来确定在期权行使时使损失函数最小化的最优对冲策略。所提出的方法只采用了经典技术,如优化算法、蒙特卡罗模拟和网格插值。最重要的是,我们选择的后向迭代方法解决了许多传统风险度量方法中固有的时间不一致性问题,迫使最优策略保持时间上的一致性,即使原始问题可能本质上不支持这种一致性。在各种数值实验中与深度对冲算法的比较显示了所提方法的效率和准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Backward hedging for American options with transaction costs

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. Specifically, the 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 proposed approach only employs classic techniques, such as an optimization algorithm, Monte Carlo simulation, and interpolation on a grid. Above all, our choice of a backward iterating approach addresses the issue of time-inconsistency inherent in many traditional risk measures, compelling the optimal strategy to maintain consistency over time, even though the original problem might not inherently support such consistency. Comparisons with the Deep Hedging algorithm in various numerical experiments showcase the efficiency and accuracy of the proposed method.

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来源期刊
Decisions in Economics and Finance
Decisions in Economics and Finance SOCIAL SCIENCES, MATHEMATICAL METHODS-
CiteScore
2.50
自引率
9.10%
发文量
10
期刊介绍: Decisions in Economics and Finance: A Journal of Applied Mathematics is the official publication of the Association for Mathematics Applied to Social and Economic Sciences (AMASES). It provides a specialised forum for the publication of research in all areas of mathematics as applied to economics, finance, insurance, management and social sciences. Primary emphasis is placed on original research concerning topics in mathematics or computational techniques which are explicitly motivated by or contribute to the analysis of economic or financial problems.
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