The asymptotic expansion of the regular discretization error of Itô integrals

Elisa Alòs and Masaaki Fukasawa

Mathematical Finance, 2021, vol. 31, issue 1, 323-365

Abstract: 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.

Date: 2021
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https://doi.org/10.1111/mafi.12292

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