AI 中文总结
本文提出一种可解释的机器学习框架，利用伊藤特征变换实现动态对冲，该方法计算高效、无需估计未来条件期望，在模拟和标普500期权实证中均表现优异，是实用的动态对冲实现框架。
AI 中文摘要
我们提出一种使用伊藤特征变换的可解释机器学习框架用于动态对冲，该变换将资产价格路径转化为一组线性特征，可通用表示时间序列上的非线性函数。我们证明，每个离散化的伊藤特征分量可仅用标的资产和现金通过简单的自融资策略完美复制，这使得伊藤特征分量成为可交易且透明的对冲基。这允许非线性衍生品收益通过特征项的线性组合近似，并通过对应的交易策略组合进行对冲。我们进一步建立了伊藤特征的新近似结果，并推导了样本内和样本外对冲误差的理论界。我们的方法计算高效、易于实现，且无需估计未来条件期望，适合实际应用。在模拟中，与神经网络基准相比，我们的方法在计算成本显著更低的同时实现了出色的样本效率。在对标普500指数期权的实证研究中，其在香草期权和路径依赖合约上均表现稳健，特征核加权版本通过将估计局部化到相似的历史市场路径进一步提升了性能。总体而言，本文将伊藤特征确定为一种实用、透明且与模型无关的动态对冲实现框架。
英文摘要
We propose an interpretable machine-learning framework for dynamic hedging using the Itô signature transform, which turns asset-price paths into a set of linear features that universally represent nonlinear functions on time-series. We show that each discretized Itô signature component can be perfectly replicated by a simple self-financing strategy using only the underlying assets and cash, which turns Itô signature components into tradable and transparent hedging bases. This allows nonlinear derivative payoffs to be approximated by linear combinations of signature terms and hedged through the corresponding combination of trading strategies. We further establish a new approximation result for the Itô signature and derive theoretical bounds for both in-sample and out-of-sample hedging errors. Our method is computationally efficient, easy to implement, and avoids the estimation of future conditional expectations, which makes it attractive for real-world applications. In simulations, our method delivers strong sample efficiency at substantially lower computational cost than neural-network benchmarks. In an empirical study of S\&P 500 index options, it performs robustly across vanilla and path-dependent contracts, with the signature-kernel weighted version providing further gains by localizing estimation to similar historical market paths. Overall, the paper identifies the Itô signature as a practical, transparent, and model-agnostic implementation framework for dynamic hedging.
