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Rock around the clock: An agent-based model of low- and high-frequency trading


We build an agent-based model to study how the interplay between low- and high-frequency trading affects asset price dynamics. Our main goal is to investigate whether high-frequency trading exacerbates market volatility and generates flash crashes. In the model, low-frequency agents adopt trading rules based on chronological time and can switch between fundamentalist and chartist strategies. By contrast, high-frequency traders activation is event-driven and depends on price fluctuations. High-frequency traders use directional strategies to exploit market information produced by low-frequency traders. Monte-Carlo simulations reveal that the model replicates the main stylized facts of financial markets. Furthermore, we find that the presence of high-frequency traders increases market volatility and plays a fundamental role in the generation of flash crashes. The emergence of flash crashes is explained by two salient characteristics of high-frequency traders, i.e., their ability to i. generate high bid-ask spreads and ii. synchronize on the sell side of the limit order book. Finally, we find that higher rates of order cancellation by high-frequency traders increase the incidence of flash crashes but reduce their duration.

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  1. The most famous example of a flash crash occurred on May 6th 2010, when the Dow Jones Industrial Average nosedived by more than 5 % in a few minutes. Financial markets are also characterized by an increasing number of mini flash crashes, a scaled down version of the “May 6th 2010” crash (Golub et al. 2012; Johnson et al. 2012).

  2. Figures vary greatly across studies depending on the market, the definition of HFT considered and the data available. See, for instance, Kirilenko et al. (2011), Aldridge (2013), Gomber and Haferkorn (2013), and SEC (2014).

  3. The uncertainty in the debate about the overall effect of HFT is probably explained by the fact that, so far, no single and concrete definition of HFT prevails (Aldridge 2013; SEC 2014). In addition, the term HFT may apply to a wide variety of trading strategies such as market making, statistical arbitrage, directional trading, electronic liquidity detection (e.g., pinging, sniffing, sniping. See, for instance, Chlistalla et al. 2011; Aldridge 2013; Gomber and Haferkorn 2013; Jones 2013; MacIntosh 2013, and further references therein).

  4. See, for instance, Farmer et al. (2005), Slanina (2008) and Pellizzari and Westerhoff (2009) for detailed studies of the effect of limit-order book models on market dynamics.

  5. See also extensive surveys on HFT in AMF (2010), Chlistalla et al. (2011), Aldridge (2013), Chordia et al. (2013), Gomber and Haferkorn (2013), Jones (2013), and MacIntosh (2013).

  6. As noted by Easley et al. (2012), HFT requires the adoption of algorithmic trading implemented through computers that natively operate on internal event-based clocks. Hence, the study of HFT cannot be reduced to its higher speed only, but it should take into account also the associated new trading paradigm. See also Aloud et al. (2013) for a modeling attempt in the same direction.

  7. For a detailed study of the statistical properties of the limit order book, cf. Bouchaud et al. (2002), Luckock (2003), and Smith et al. (2003).

  8. The price of an executed contract is the average between the matched bid and ask quotes. Note that when both an LF and HF agents send a buy (sell) order with the same price, the order of the LF agent is executed first. The simulation results discussed below do not substantially change when we assume that, in such a limit case, HF agents’ orders have priority over LF traders’ ones. See Appendix 2 for further detail.

  9. The results presented in Section 3 also hold when the market price is defined as the highest or average price of executed transactions in the trading session.

  10. See also Alfarano et al. (2010) for a model with different time horizons.

  11. We assume that N H <N L . The proportion of HF agents vis-à-vis LF ones is in line with empirical evidence (Kirilenko et al. 2011; Paddrik et al. 2011).

  12. On the case for moving away from chronological time in modeling financial series, see Mandelbrot and Taylor (1967), Clark (1973), and Ané and Geman (2000).

  13. In the computation of the mean of the Poisson distribution, the relevant market volumes are weighted by the parameter 0<λ<1.

  14. 14 Simulation exercises in the baseline scenario reveal that the strategies adopted by HF traders are able to generate positive profits, thus justifying their adoption by HF agents in the model. In addition, simulation results indicate that HF traders’ average profits are significantly higher than those of LF traders.

  15. See Windrum et al. (2007) for a discussion of this approach.

  16. The power-law exponent was estimated using the freely available “power-law package” and based on the procedure developed in Clauset et al. (2009).

  17. Interestingly, our model is also able to generate flash peaks, defined as spikes in asset price of at least 5 % followed by a phase of return to pre-peak price levels of 30 periods at maximum. See, for instance, Johnson et al. (2013) for empirical evidence on the number and duration of flash peaks as well as flash crashes in financial data. The model also reproduces another relevant and recent stylized fact observed during flash crashes, namely the negative correlation between price and volumes (see, e.g., Kirilenko et al. 2011).

  18. See Farmer et al. (2004) for empirical evidence on the relation between liquidity fluctuations and large price changes.

  19. Notice that the concentration of LF orders on the buy side may occur irrespectively of the particular distribution of strategies within this group of agents.

  20. See Haldane (2014) for a discussion of the different proposed explanations of flash crashes.

  21. We also carried out simulations for γ H>20. The above patterns are confirmed. Interestingly, flash crashes completely disappear when the order cancellation rate is very low.

  22. Haldane (2014) also emphasizes that there is a trade-off when deciding whether to impose resting rules (market efficiency versus stability).

  23. Because of space constraints, we do not provide the figures concerning the whole set of stylized facts reproduced by the model. These figures are, however, available from the authors upon request


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We are grateful to Sylvain Barde, Francesca Chiaromonte, Jean-Luc Gaffard, Nobi Hanaki, Alan Kirman, Fabrizio Lillo, Frank Westerhoff, and two anonymous referees for stimulating comments and fruitful discussions. We also thank the participants of the Workshop on Heterogeneity and Networks in (Financial) Markets in Marseille, March 2013, of the EMAEE conference in Sophia Antipolis, May 2013, of the WEHIA conference in Reykiavik, June 2013, of the 2013 CEF conference in Vancouver, July 2013 and of the SFC workshop in Limerick, August 2013 where earlier versions of this paper were presented. All usual disclaimers apply. The authors gratefully acknowledge the financial support of the Institute for New Economic Thinking (INET) grants #220, “The Evolutionary Paths Toward the Financial Abyss and the Endogenous Spread of Financial Shocks into the Real Economy”.

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Correspondence to Sandrine Jacob Leal.


Appendix 1: Parameters

Table 4 Parameters values in the baseline scenario

Appendix 2: Model results under alternative time-order priority

In the paper, we assume that HF orders are inserted in the book after LF ones and before the actual matching takes place. As discussed in Section 2.1, this allows us to account for the low-latency feature of high-frequency trading strategies. Accordingly, when both an LF and HF agents send a buy (sell) order with the same price, the order of the LF agent is executed first (see footnote 8). In order to check the sensitivity of our results to the latter assumption, we have also performed simulations assuming that time priority was instead given to HF orders. The results of these simulations show first that all the properties of the model are robust to this alternative assumption. For instance, Fig. 11 shows that zero-autocorrelation of returns is reproduced by the model also in this alternative scenario. The same holds for the presence of volatility clustering (see Fig. 12).Footnote 23 Finally, Tables 5 and 6 report, respectively, the results on market statistics and agents’ order aggressiveness. The figures in both tables confirm, as explained in footnote 8, that these model’s results do not substantially change when we assume that where two orders have the same price, HF agents’ orders have priority over LF traders’ ones.

Fig. 11
figure 11

Baseline scenario with time-order priority given to HF orders. Price-returns sample autocorrelation function (solid line) together with 95 % confidence bands (dashed lines). Values are averages across 50 independent Monte-Carlo runs

Fig. 12
figure 12

Baseline scenario with time-order priority given to HF orders. Sample autocorrelation functions of absolute price returns (solid line) together 95 % confidence bands (dashed lines). Values are averages across 50 independent Monte-Carlo runs

Table 5 Market statistics for baseline scenario with time-order priority given to HF orders
Table 6 Orders’ aggressiveness ratios for different categories of traders and different market phases

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Jacob Leal, S., Napoletano, M., Roventini, A. et al. Rock around the clock: An agent-based model of low- and high-frequency trading. J Evol Econ 26, 49–76 (2016).

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  • Agent-based models
  • Limit order book
  • High-frequency trading
  • Low-frequency trading
  • Flash crashes
  • Market volatility

JEL Classification

  • G12
  • G01
  • G14
  • C63