A Hawkes process analysis of high-frequency price endogeneity and market efficiency

ABSTRACT

We use the Hawkes process to model the high-frequency price process of 108 stocks in the Chinese stock market, in order to understand the endogeneity of price changes and the mechanism of information processing. Using a piece-wise constant exogenous intensity, we employ non-parametric estimation, residual analysis, and Bayesian Information Criterion (BIC) to determine that a power-law kernel is the most appropriate for our data. We propose the internal branching ratio to represent endogeneity within a finite interval. The branching ratio tends to be higher after the market opens and before the market closes, with a mean value of around 0.81, suggesting significant endogeneity in price changes. In addition, we explore the relationship between branching ratios and stock characteristics using panel regression. Higher branching ratios are associated with lower levels of price efficiency at high, but not low, frequencies. Finally, the branching ratio increases over time without significant impact from COVID-19.

KEYWORDS:

• Market efficiency
• price endogeneity
• Hawkes process
• branching ratio
• Kernel function
• Chinese stock market

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 For discussions on this topic, see, for example, Filimonov and Sornette (2012, 2015), Hardiman, Bercot, and Bouchaud (2013), Filimonov et al. (2014), Wheatley, Wehrli, and Sornette (2019), and Wehrli, Wheatley, and Sornette (2021).

2 According to data from World Bank (https://data.worldbank.org), as of 2020, the total value of China's stock market has climbed to a record high of more than USD 12.2 trillion, making it the second-largest in the world after that of the US.

3 Recent empirical evidence shows that the world has started to move from a unipolar to a multipolar financial system in which China plays an increasingly central role (Billio et al. 2022; McKibbin and Fernando 2021).

4 See, for example, Z. Li et al. (2018) and Gao and Ding (2019).

5 Available at: http://www.szsi.cn/cpfw/overseas/market/historical/.

6 CSI 300 is the Chinese equivalent of S&P 500 and it contains 300 securities with large market capitalization and good liquidity. More details are available at https://www.csindex.com.cn/#/indices/family/detail?indexCode=000300.

7 This includes January 9th, March 14th, and March 15th, 2019.

8 The continuous bidding period for each trading day is from 9:30–11:30 am and 1:00–2:57 pm, which amounts to a total of 3 hours and 57 minutes. To make the morning and afternoon sessions symmetrical for convenience purposes, we expand the afternoon session to 2 hours and simply record the length of a day's trading time as four hours. The last three-minute of the trading day, therefore, do not contain any events. This choice does not bias subsequent estimates because we have detrended the process.

9 Specifically, we redistribute the n events with the same timestamp at t, $t+\mathrm{\Delta }/n$, $t+2\mathrm{\Delta }/n$, …, $t+(n-1)\mathrm{\Delta }/n$, where $\mathrm{\Delta }=10\mathrm{ms}$ is the resolution of our time measurements. Here we adopt a deterministic redistribution approach to improve the reproducibility of our results. In several studies (Filimonov and Sornette 2012, 2015; Hardiman, Bercot, and Bouchaud 2013; Wehrli, Wheatley, and Sornette 2021), the event timestamps are distributed randomly in each interval. In Section 6.1, we verify that our approach leads to very similar estimation results compared to the random redistribution method.

10 According to the selection of the number of segments later in Section 4.2, it is sufficient to divide a day into four segments for estimation.

11 Section 6.2 provides an overview of the impact of hyper-parameter selection on estimation results.

12 To verify that high-frequency traders are driving this phenomenon, one needs transaction-level data with labels of high-frequency traders, which is beyond the scope of this article.

Additional information

Funding

We thank an anonymous editor and two anonymous reviewers for very helpful comments. Research support from the National Key R&D Program of China (2022YFA1007900), the National Natural Science Foundation of China (12271013), and the Fundamental Research Funds for the Central Universities (Peking University) is gratefully acknowledged.

Notes on contributors

Jingbin Zhuo

Jingbin Zhuo is a student at Peking University.

Yufan Chen

Yufan Chen is a student at Peking University.

Bang Zhou

Bang Zhou is a student at Peking University.

Baiming Lang

Baiming Lang is a student at Peking University.

Lan Wu

Lan Wu is a professor at Peking University.

Ruixun Zhang

Ruixun Zhang is an assistant professor at Peking University.