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The asymptotic expansion of the regular discretization error of Itô integrals

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  • Elisa Alòs
  • Masaaki Fukasawa

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.

Suggested Citation

  • Elisa Alòs & Masaaki Fukasawa, 2021. "The asymptotic expansion of the regular discretization error of Itô integrals," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 323-365, January.
    • Handle: RePEc:bla:mathfi:v:31:y:2021:i:1:p:323-365
    DOI: 10.1111/mafi.12292
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    References listed on IDEAS

    as
    1. Carole Bernard & Zhenyu Cui, 2014. "Prices and Asymptotics for Discrete Variance Swaps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(2), pages 140-173, April.
    2. Mark Podolskij & Mathias Vetter, 2009. "Understanding limit theorems for semimartingales: a short survey," CREATES Research Papers 2009-47, Department of Economics and Business Economics, Aarhus University.
    3. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
    4. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    5. Mark Podolskij & Bezirgen Veliyev & Nakahiro Yoshida, 2018. "Edgeworth expansion for Euler approximation of continuous diffusion processes," CREATES Research Papers 2018-28, Department of Economics and Business Economics, Aarhus University.
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