Heterogeneous speculators and stock market dynamics: a simple agent-based computational model

Abstract

We propose a simple agent-based computational model in which speculators’ trading behavior may cause bubbles and crashes, excess volatility, serially uncorrelated returns, fat-tailed return distributions and volatility clustering, thereby replicating five important stylized facts of stock markets. Since each speculator bets on his own (technical and fundamental) trading signals, stock prices are excessively volatile and oscillate erratically around their fundamental value. However, speculators’ heterogeneity occasionally vanishes, e.g. due to panic-induced herding behavior, yielding extreme returns. Lasting regimes with high volatility originate from the fact that speculators extract stronger trading signals out of past stock price movements when stock prices fluctuate strongly. Simulations furthermore suggest that circuit breakers may be an effective tool to combat financial market turbulences.

KEYWORDS:

• Stock markets
• stylized facts
• agent-based computational models
• technical and fundamental analysis
• circuit breakers
• econophysics

JEL CLASSIFICATIONS:

• C63
• D84
• G15

Acknowledgement

We would like to thank two anonymous referees and Giulia Iori for their valuable feedback. This research was carried out in the Bamberg Doctoral Research Group on Behavioral Macroeconomics (BaGBeM) supported by the Hans-Böckler Foundation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 According to Murphy (1999), the reliability of technical trading signals increases with the trading volume of a stock market, i.e. a high trading volume indicates that the current trading signal is strong whereas a low trading volume indicates that the current trading signal is weak. Since simulations reveal that our model produces a high contemporaneous correlation between trading volume and volatility, an interesting model extension could be to condition speculators’ trading intensity on the trading volume of the stock market. See Westerhoff (2006) for an example in that direction.

2 A well-known example in this respect concerns the stock market crash of October 1987, which, according to Greenwald and Stein (1991), Harris (1998) and Shiller (2015), was at least partially triggered by computer (program) trading, and could have been stopped by circuit breakers. More recent examples include the occurrence of so-called flash crashes, amplified by high-frequency traders who follow computerized trading systems. See Jacob Leal et al. (2016) and Jacob Leal and Napoletano (2019) for empirical evidence and interesting modeling approaches. Gomber and Zimmermann (2018) and Vassiliadis and Dounias (2018) provide insightful overviews of complex (algorithmic) trading systems.

3 As we will see in the next section, however, one condition may already be sufficient for our model to produce extreme price changes and, consequently, fat-tailed return distributions. We remark that we also experimented with other conditions. For instance, similar dynamics to those discussed in the next section may be observed if (8) is replaced by $C_t=g{C}_{t-1}+(1-g)(P_t-P_{t-1}{)}^2$, where $0<g<1$ is a memory parameter. In relation to (6), however, our simulations suggest that the memory parameter has to be set to a rather low value, say $g=0.05$, implying that coordination among market participants critically hinges on the stock market’s short-run behavior. To save one parameter, we opted for specification (8). Of course, this aspect deserves more attention in future work, in particular along the lines indicated above.

4 The excess demand also increases with the number of speculators. For $a=\alpha /N$ and $N\to \mathrm{\infty }$, however, the price adjustment equation reads $P_{t+1}=P_t+\alpha \left\{(b(P_t-P_{t-1})+c(F-P_t))+{\sigma }_t\sqrt{{\rho }_t}{\epsilon }_t\right\}$. Hence, it is possible to rescale our model such that its dynamics does not depend on the number of speculators. While we prefer to keep $N$ as a model parameter, it might be worthwhile to try to endogenize the number of (active) speculators in future work. See Iori (2002), Alfi et al. (2009), Blaurock, Schmitt, and Westerhoff (2018) and Dieci, Schmitt, and Westerhoff (2018) for examples in this direction.

5 Bubbles and crashes are difficult to identify in real stock markets. However, Galbraith (1994), Kindleberger and Aliber (2011) and Shiller (2015) stress that bubbles and crashes do exist in these markets. See Schmitt and Westerhoff (2017c) and Majewski, Ciliberti, and Bouchaud (2020) for attempts on how to capture the mispricing of actual stock markets.

6 Such estimates are representative for many different financial markets, see, e.g. Gopikrishnan et al. (1999) and Plerou et al. (1999).

7 Of course, other estimation methods may also be useful, see, e.g., the work by Lamperti, Roventini, and Sani (2018), Platt (2020), Kukacka and Kristoufek (2020) and Bertschinger and Mozzhorin (2020).

8 The famous “factor 2” rule by Black (1986, 533) implies that the stock “price is more than half of value and less than twice value”. For our case, simulated stock prices should thus fluctuate in the interval $0.5<F=1<2$.

9 Note that a high correlation between speculators’ trading behavior does not always lead to a strong stock price change. For this to be the case, speculators have to coordinate on a significant trading signal.

10 Note that speculators’ trading intensity (variance) may remain high for extended periods of time, thereby producing lasting volatility outbreaks, while their coordination (correlation) spikes only occasionally, forming the base for rare but extreme returns. We discuss this aspect in more detail in Appendix A.2.

11 As pointed out by an anonymous referee, it might also be worthwhile to use our model to study the effects of margin requirements, leverage cycles and short-selling constraints. For inspiring work in this direction, see, for instance, Poledna et al. (2014), Aymanns et al. (2016) and Sng, Zhang, and Zheng (2020). Aymanns et al. (2018) and Westerhoff and Franke (2018) discuss in more detail how policymakers may use models with heterogeneous interacting agents as test beds to evaluate the effectiveness of regulatory policies.

12 Our model is also able to generate extreme returns for lower values of ${\sigma }_t^2=0.000003$. However, we found that this number matches actual tail indices quite well.