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Transform analysis for Hawkes processes with applications in dark pool trading

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  • Xuefeng Gao
  • Xiang Zhou
  • Lingjiong Zhu

Abstract

Hawkes processes are a class of simple point processes that are self-exciting and have a clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general function and the jump sizes of the intensity process are independent and identically distributed nonnegative random variables. This Hawkes model is non-Markovian in general. We obtain closed-form formulas for the Laplace transform, moments and the distribution of the Hawkes process. To illustrate the applications of our results, we use the Hawkes process to model the clustered arrival of trades in a dark pool and analyse various performance metrics including time-to-first-fill, time-to-complete-fill and the expected fill rate of a resting dark order.

Suggested Citation

  • Xuefeng Gao & Xiang Zhou & Lingjiong Zhu, 2018. "Transform analysis for Hawkes processes with applications in dark pool trading," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 265-282, February.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:2:p:265-282
    DOI: 10.1080/14697688.2017.1403151
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    Citations

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    Cited by:

    1. Pankaj Kumar, 2021. "Deep Hawkes Process for High-Frequency Market Making," Papers 2109.15110, arXiv.org.
    2. Yang Shen & Bin Zou, 2021. "Mean-Variance Portfolio Selection in Contagious Markets," Papers 2110.09417, arXiv.org.
    3. Thomas Deschatre & Pierre Gruet, 2021. "Electricity intraday price modeling with marked Hawkes processes," Papers 2103.07407, arXiv.org, revised Mar 2021.
    4. Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122, arXiv.org.
    5. Hillairet, Caroline & Réveillac, Anthony & Rosenbaum, Mathieu, 2023. "An expansion formula for Hawkes processes and application to cyber-insurance derivatives," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 89-119.
    6. Timoth'ee Fabre & Ioane Muni Toke, 2024. "Neural Hawkes: Non-Parametric Estimation in High Dimension and Causality Analysis in Cryptocurrency Markets," Papers 2401.09361, arXiv.org, revised Jan 2024.
    7. Jiwook Jang & Rosy Oh, 2020. "A Bivariate Compound Dynamic Contagion Process for Cyber Insurance," Papers 2007.04758, arXiv.org.
    8. Raviar Karim & Roger J. A. Laeven & Michel Mandjes, 2021. "Exact and Asymptotic Analysis of General Multivariate Hawkes Processes and Induced Population Processes," Papers 2106.03560, arXiv.org.
    9. Ulrich Horst & Wei Xu, 2024. "Functional Limit Theorems for Hawkes Processes," Papers 2401.11495, arXiv.org.

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