Rule-based trading on an order-driven exchange: a reassessment

Abstract

A core research area of computational behavioral finance investigates emergent price dynamics when heterogeneous traders follow a mix of rule-based strategies and interact indirectly through a limit order book. This paper offers a detailed specification of such a model in order to raise questions about some previous findings. The questions force a comprehensive reconsideration of the price dynamics of a well-known model. This leads to a surprising clarification of the contributions of various trading strategies to market outcomes: a popular characterization of chartism proves largely irrelevant for price dynamics. We also shed new light on the volume-volatility relationship, and provide improved visualizations to expose market behavior.

Keywords:

• Chartism
• Price dynamics
• Return volatility
• Trade volume
• Market microstructure
• Limit order book
• Computational behavioral finance

JEL Classifications:

• G12
• G17
• C63

Open Scholarship

This article has earned the Center for Open Science badges for Open Data and Open Materials through Open Practices Disclosure. The data and materials are openly accessible at https://figshare.com/s/e02cbb7790ab902eb72e.

Acknowledgments

Equal authorship; the authors are in alphabetical order. We thank Ben Dempe, two anonymous referees, and an Associate Editor for helpful suggestions. We particularly thank Blake LeBaron for useful discussions and kind encouragement.

Disclosure statement

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

Supplemental data

Supplemental data for this article can be accessed online at http://dx.doi.org/10.1080/14697688.2023.2270711.

Notes

1 If all floating point prices were acceptable, the market would not see common prices across orders. However, a market in a security typically has a tick size, which is the minimal price increment. In addition, order prices outside an acceptable (wide) trading range are typically rejected. Chiarella and Iori (2002, p. 348) address this by introducing a pre-specified grid of possible prices, based on the tick size (Δ). (Unfortunately, they do not document the minimum and maximum values of this grid.) We follow this practice, specifying a (wide) range of possible prices, from 1% to 200% of the reference fundamental price.

2 In order to produce the plausible price dynamics required of a replication, their reported parameterization must be substantially rescaled during the price-forecast computation, as exposed by Chiarella et al. (2009) and especially Pellizzari and Westerhoff (2009). In addition, Chiarella et al. (2009) constrain the weights to be positive, thereby removing contrarians from the chartist traders. The consequences of such a change are discussed in the supplement to our paper.

3 This paper uses the fundamental price to initialize the price history. Results with a random initial price history are similar, so the model appears robust to this choice.

4 The original code is unavailable (G. Iori, personal communication, 2020). Find code for the present paper at https://figshare.com/s/e02cbb7790ab902eb72e.

5 Our supplement to this paper provides detailed documentation of this claim.

6 We base this choice on Chiarella and Iori (2002, p. 351–352), which describes the average spot volatility as being in the neighborhood of $2\times {10}^{-4}$. This appears to be roughly the value of volatility indicated at around $\lambda =0.5$ in Chiarella and Iori (2002, figure 3). However, there are two other imaginable measures for a simulation of N periods of T time steps per period. One is a simple average of CI's time-period volatilities, as described by (6(6) ${\sigma }^T=\frac{1}{T}\sum _{t=1}^T\left|\frac{p_t-p_{t-1}}{p_{t-1}}\right|\sqrt{T}$(6) ). That produces $\begin{array}{rl}& \frac{1}{N}\sum _{n=1}^N\left(\frac{1}{\sqrt{T}}\sum _{i=1}^T|\frac{p_{(n-1)\ast T+i}}{p_{(n-1)\ast T+i-1}}-1|\right)\\ & =\frac{1}{N\sqrt{T}}\sum _{n=1}^N\sum _{i=1}^T|\frac{p_{(n-1)\ast T+i}}{p_{(n-1)\ast T+i-1}}-1|\end{array}$ The other is to apply (6(6) ${\sigma }^T=\frac{1}{T}\sum _{t=1}^T\left|\frac{p_t-p_{t-1}}{p_{t-1}}\right|\sqrt{T}$(6) ) directly to the entire price trajectory. $\frac{1}{\sqrt{NT}}\sum _{t=1}^{NT}|\frac{p_t}{p_{t-1}}-1|=\frac{1}{\sqrt{NT}}\sum _{n=1}^N\sum _{i=1}^T|\frac{p_{(n-1)\ast T+i}}{p_{(n-1)\ast T+i-1}}-1|$ Clearly the only difference between these measures is scaling, so the choice between them is arbitrary and inconsequential.

7 This means that the first, fifth, and fourth subfigures correspond to the left column of Chiarella and Iori (2002, figure 1).

8 More precisely, aside from artefacts of the series construction, the logarithm of the market price should resemble a random walk in this case.

9 For this reason, altering the weighting schema to emphasize chartism fails, even when imposing an unreasonably large relative weight on chartism. The supplement to this paper provides additional exploration of these issues.

10 Attentive readers will note the scale change in the last subfigure of Chiarella and Iori (2002, figure 1). See the supplement to this paper for further explorations.

11 The returns are calculated from the closing prices of Apple Inc. stock (ticker: AAPL) over the 1001 trading days between May 4th, 2016 to April 24, 2020. (Last accessed 2023-10-04.)

12 We use a lag length of 10 periods for both tests. However, we also deployed the test using the optimal lag selection methodology prescribed in Escanciano and Lobato (2009). The optimal lag for the Ljung-Box test for the simulated returns was 1, and for AAPL stock was 30. The optimal lag for the McLeod-Li test for the simulated returns was 6, and for AAPL stock was 29. The results were qualitatively the same in all cases as those reported in table 2.

13 Box plots are for trade counts seen in at least 10 periods.

14 Figure 5 describes the price series, which uses the book's midpoint price if no new trade executes. More market participation makes it more likely that a new bid or ask will beat the top of the book, which increases measured volatility.