We study an Edgeworth‐type refinement of the central limit theorem for the discretization error of Itô integrals. Toward this end, we introduce a new approach, based on the anticipating Itô formula. This alternative technique allows us to compute explicitly the terms of the corresponding expansion formula. Two applications to finance are given; the asymptotics of discrete hedging error under the Black–Scholes model and the difference between continuously and discretely monitored variance swap payoffs under stochastic volatility models.

中文翻译：

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Itô积分正则离散误差的渐近展开

我们针对Itô积分的离散化误差研究了中心极限定理的Edgeworth型细化。为此，我们基于预期的Itô公式引入了一种新方法。这种替代技术使我们可以显式计算相应扩展公式的项。给出了两个金融应用程序；Black-Scholes模型下离散对冲误差的渐近性，以及随机波动率模型下连续和离散监测的方差互换收益之间的差异。