IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v31y2021i1p323-365.html
   My bibliography  Save this article

The asymptotic expansion of the regular discretization error of Itô integrals

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12292
    Download Restriction: no
    File URL: https://libkey.io/10.1111/mafi.12292?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    4. 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.
    5. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    2. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org.
    3. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    4. Prosper Dovonon & Sílvia Gonçalves & Ulrich Hounyo & Nour Meddahi, 2019. "Bootstrapping High-Frequency Jump Tests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 793-803, April.
    5. Reisenhofer, Rafael & Bayer, Xandro & Hautsch, Nikolaus, 2022. "HARNet: A convolutional neural network for realized volatility forecasting," CFS Working Paper Series 680, Center for Financial Studies (CFS).
    6. Tim Bollerslev & Jia Li & Yuan Xue, 2018. "Volume, Volatility, and Public News Announcements," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2005-2041.
    7. Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2019. "Is Volatility Rough ?," Papers 1905.04852, arXiv.org, revised May 2019.
    8. Yamagishi, Hayate & Yoshida, Nakahiro, 2023. "Order estimate of functionals related to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 490-543.
    9. Alexander, Carol & Rauch, Johannes, 2021. "A general property for time aggregation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 536-548.
    10. Jim Griffin & Jia Liu & John M. Maheu, 2021. "Bayesian Nonparametric Estimation of Ex Post Variance [Out of Sample Forecasts of Quadratic Variation]," Journal of Financial Econometrics, Oxford University Press, vol. 19(5), pages 823-859.
    11. Kim, Seong-Tae & Kim, Jeong-Hoon, 2020. "Stochastic elasticity of vol-of-vol and pricing of variance swaps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 420-440.
    12. Andersen, Torben G. & Cebiroglu, Gökhan & Hautsch, Nikolaus, 2017. "Volatility, information feedback and market microstructure noise: A tale of two regimes," CFS Working Paper Series 569, Center for Financial Studies (CFS).
    13. Flood, M. D. & Jagadish, H. V. & Raschid, L., 2016. "Big data challenges and opportunities in financial stability monitoring," Financial Stability Review, Banque de France, issue 20, pages 129-142, April.
    14. Rene Carmona & Kevin Webster, 2019. "Applications of a New Self-Financing Equation," Papers 1905.04137, arXiv.org.
    15. Podolskij, Mark & Veliyev, Bezirgen & Yoshida, Nakahiro, 2017. "Edgeworth expansion for the pre-averaging estimator," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3558-3595.
    16. Yuping Song & Weijie Hou & Zhengyan Lin, 2022. "Double Smoothed Volatility Estimation of Potentially Non‐stationary Jump‐diffusion Model of Shibor," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 53-82, January.
    17. Yoshida, Nakahiro, 2023. "Asymptotic expansion and estimates of Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 176-248.
    18. Bibinger, Markus & Neely, Christopher & Winkelmann, Lars, 2019. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 158-184.
    19. Casini, Alessandro & Perron, Pierre, 2021. "Continuous record Laplace-based inference about the break date in structural change models," Journal of Econometrics, Elsevier, vol. 224(1), pages 3-21.
    20. Maria Elvira Mancino & Tommaso Mariotti & Giacomo Toscano, 2022. "Asymptotic Normality for the Fourier spot volatility estimator in the presence of microstructure noise," Papers 2209.08967, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:31:y:2021:i:1:p:323-365. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.